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Results in
*Proceedings of the American Mathematical Society*: 36,957

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Published: 4 March 2008

Proceedings of the American Mathematical Society, Volume 136, pp 2597-2607; https://doi.org/10.1090/s0002-9939-08-09163-6

**Abstract:**

Let denote a Lévy process in with exponent . Taylor (1986) proved that the packing dimension of the range is given by the index

Published: 8 February 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2937-2952; https://doi.org/10.1090/proc/13961

**Abstract:**

We present a proof of the local Hölder regularity of the horizontal derivatives of weak solutions to the p p -Laplace equation in the Heisenberg group H 1 \mathbb {H}^1 for p > 4 p>4 .

Published: 30 October 2017

Proceedings of the American Mathematical Society, Volume 146, pp 1243-1256; https://doi.org/10.1090/proc/13831

Published: 7 December 2017

Proceedings of the American Mathematical Society, Volume 146, pp 1231-1242; https://doi.org/10.1090/proc/13814

**Abstract:**

In this paper, we prove uniqueness of solutions of mean field equations with general boundary conditions for the critical and subcritical total mass regime, extending the earlier results for null Dirichlet boundary condition. The proof is based on new Bol's inequalities for weak radial solutions obtained from rearrangement of the solutions.

Published: 8 November 2018

Proceedings of the American Mathematical Society, Volume 147, pp 583-596; https://doi.org/10.1090/proc/13962

Published: 16 January 2018

Proceedings of the American Mathematical Society, Volume 146, pp 1963-1976; https://doi.org/10.1090/proc/13970

**Abstract:**

We restrict irreducible characters of finite groups of degree divisible by p p to their Sylow p p -subgroups and study the number of linear constituents.

Published: 16 February 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2663-2677; https://doi.org/10.1090/proc/13964

Published: 8 February 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2785-2796; https://doi.org/10.1090/proc/13963

**Abstract:**

We construct three elements in the kernel of the tame symbol on families of quartic curves. We show that these elements are integral under certain conditions on the parameters. Moreover, we prove that these elements are in general linearly independent by calculating the limit of the regulator.

Published: 13 November 2018

Proceedings of the American Mathematical Society, Volume 147, pp 629-635; https://doi.org/10.1090/proc/13965

Published: 4 April 2011

Proceedings of the American Mathematical Society, Volume 139, pp 4513-4520; https://doi.org/10.1090/s0002-9939-2011-10888-8

**Abstract:**

We define the Thurston-Bennequin polytope of a two-component link as the convex hull of all pairs of integers that arise as framings of a Legendrian representative. The main result of this paper is a description of the Thurston-Bennequin polytope for two-bridge links. As an application, we construct non-quasipositive surfaces in $\mathbb {R}^3$ all of whose sub-annuli are quasipositive.

Published: 4 April 2011

Proceedings of the American Mathematical Society, Volume 139, pp 4343-4349; https://doi.org/10.1090/s0002-9939-2011-10840-2

**Abstract:**

A new result on existence of nonzero positive solutions of systems of second order elliptic boundary value problems is obtained under some sublinear conditions involving the principle eigenvalues of the corresponding linear systems. Results on eigenvalue problems of such elliptic systems are derived and generalize some previous results on the eigenvalue problems of systems of Laplacian elliptic equations. Applications of our results are given to two such systems with specific nonlinearities.

Published: 1 October 2011

Proceedings of the American Mathematical Society, Volume 139, pp 3697-3697; https://doi.org/10.1090/s0002-9939-2011-10772-x

**Abstract:**

The so-called Cayley hypersurface, constructed by Eastwood and Ezhov, is a higher-dimensional extension of the classical Cayley surface. In this paper, we establish a differential geometric characterization of the Cayley hypersurface, which is an answer to Eastwood and Ezhov's question.

Published: 5 April 2011

Proceedings of the American Mathematical Society, Volume 139, pp 4361-4368; https://doi.org/10.1090/s0002-9939-2011-11022-0

**Abstract:**

The main goal of this paper is to extend in R n \mathbb {R}^n a result of Seeley on eigenfunction expansions of real analytic functions on compact manifolds. As a counterpart of an elliptic operator in a compact manifold, we consider in R n \mathbb {R}^n a selfadjoint, globally elliptic Shubin type differential operator with spectrum consisting of a sequence of eigenvalues λ j , j ∈ N , \lambda _j, {j\in \mathbb N}, and a corresponding sequence of eigenfunctions u j , j ∈ N u_j, j\in \mathbb N , forming an orthonormal basis of L 2 ( R n ) . L^2(\mathbb R^n). Elements of Schwartz S ( R n ) \mathcal S(\mathbb R^n) , resp. Gelfand-Shilov S 1 / 2 1 / 2 S^{1/2}_{1/2} spaces, are characterized through expansions ∑ j a j u j \sum _ja_ju_j and the estimates of coefficients a j a_j by the power function, resp. exponential function of λ j \lambda _j .

Published: 1 December 2011

Proceedings of the American Mathematical Society, Volume 139, pp 4461-4466; https://doi.org/10.1090/s0002-9939-2011-11009-8

**Abstract:**

In this paper we construct a family of subspace arrangements whose intersection lattices have the shape of Pascal's triangle. We prove that even though the intersection lattices are not geometric, the complex complement of the arrangements are rationally formal.

Published: 5 April 2011

Proceedings of the American Mathematical Society, Volume 139, pp 4445-4459; https://doi.org/10.1090/s0002-9939-2011-10915-8

**Abstract:**

Let $k:\mathbb {C}\to \mathbb {R}$ be a smooth given function. A $k$ -loop is a closed curve $u$ in $\mathbb {C}$ having prescribed curvature $k(p)$ at every point $p\in u$ . We use variational methods to provide sufficient conditions for the existence of $k$ -loops. Then we show that a breaking symmetry phenomenon may produce multiple $k$ -loops, in particular when $k$ is radially symmetric and somewhere increasing. If $k>0$ is radially symmetric and non-increasing, we prove that any embedded $k$ -loop is a circle; that is, round circles are the only convex loops in $\mathbb {C}$ whose curvature is a non-increasing function of the Euclidean distance from a fixed point. The result is sharp, as there exist radially increasing curvatures $k>0$ which have embedded $k$ -loops that are not circles.

Published: 1 December 2011

Proceedings of the American Mathematical Society, Volume 139, pp 4173-4179; https://doi.org/10.1090/s0002-9939-2011-10837-2

**Abstract:**

Let be a geometrically connected smooth projective curve of genus over . Let be the coarse moduli space of geometrically stable vector bundles over of rank and determinant , where is a real point of the Picard variety . If , then let be odd. We compute the Brauer group of .

Published: 23 October 2017

Proceedings of the American Mathematical Society, Volume 146, pp 1181-1187; https://doi.org/10.1090/proc/13792

Published: 12 October 2017

Proceedings of the American Mathematical Society, Volume 146, pp 581-587; https://doi.org/10.1090/proc/13698

**Abstract:**

We prove that if is a countable group without a subgroup isomorphic to that acts faithfully and minimally by orientation-preserving homeomorphisms on the circle, then it has a free orbit. We give examples showing that this does not hold for actions by homeomorphisms of the line.

Published: 26 January 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2577-2584; https://doi.org/10.1090/proc/13946

Published: 8 January 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2173-2180; https://doi.org/10.1090/proc/13945

Published: 28 February 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2585-2600; https://doi.org/10.1090/proc/13960

Published: 8 February 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2601-2616; https://doi.org/10.1090/proc/13956

Published: 16 February 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2359-2372; https://doi.org/10.1090/proc/13951

Published: 16 February 2018

Proceedings of the American Mathematical Society, Volume 146, pp 3085-3096; https://doi.org/10.1090/proc/13957

Published: 16 July 2021

Proceedings of the American Mathematical Society, Volume 149, pp 4057-4066; https://doi.org/10.1090/proc/13959

**Abstract:**

We prove that for any dimension function $h$ with $h \prec x^d$ and for any countable set of linear patterns, there exists a compact set $E$ with $\mathcal {H}^h(E)>0$ avoiding all the given patterns. We also give several applications and recover results of Keleti, Maga, and Máthé.

Published: 16 February 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2773-2784; https://doi.org/10.1090/proc/13958

**Abstract:**

Let K K be a number field with ring of integers O K \mathcal {O}_K , and let { f k } k ∈ N \{f_k\}_{k\in \mathbb {N}} be a sequence of monic polynomials in O K [ x ] \mathcal {O}_K[x] such that for every n ∈ N n\in \mathbb {N} , the composition f ( n ) = f 1 ∘ f 2 ∘ … ∘ f n f^{(n)}=f_1\circ f_2\circ \ldots \circ f_n is irreducible. In this paper we show that if the size of the Galois group of f ( n ) f^{(n)} is large enough (in a precise sense) as a function of n n , then the set of primes p ⊆ O K \mathfrak {p}\subseteq \mathcal {O}_K such that every f ( n ) f^{(n)} is irreducible modulo p \mathfrak {p} has density zero. Moreover, we prove that the subset of polynomial sequences such that the Galois group of f ( n ) f^{(n)} is large enough has density 1, in an appropriate sense, within the set of all polynomial sequences.

Published: 12 January 2018

Proceedings of the American Mathematical Society, Volume 146, pp 1389-1399; https://doi.org/10.1090/proc/13955

Published: 28 September 2017

Proceedings of the American Mathematical Society, Volume 146, pp 15-28; https://doi.org/10.1090/proc/13597

**Abstract:**

We prove that the multiplicities of certain maximal weights of -modules are counted by pattern avoidance on words. This proves and generalizes a conjecture of Jayne-Misra. We also prove similar phenomena in types and . Both proofs are applications of Kashiwara's crystal theory.

Published: 1 February 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2555-2562; https://doi.org/10.1090/proc/13942

Published: 17 April 2018

Proceedings of the American Mathematical Society, Volume 146, pp 3217-3232; https://doi.org/10.1090/proc/13941

Published: 23 October 2017

Proceedings of the American Mathematical Society, Volume 146, pp 555-569; https://doi.org/10.1090/proc/13680

**Abstract:**

In this paper, weighted norm inequalities for multilinear Fourier multipliers with Besov regularity are discussed. As a result, we obtain a limiting case of Hörmander type multiplier theorem for multilinear operators.

Published: 7 August 2018

Proceedings of the American Mathematical Society, Volume 146, pp 4563-4570; https://doi.org/10.1090/proc/13944

Published: 16 February 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2381-2393; https://doi.org/10.1090/proc/13943

**Abstract:**

The equivariant Hilbert series of an ideal generated by an orbit of a monomial under the action of the monoid ${\textrm {Inc} (\mathbb {N})}$ of strictly increasing functions is determined. This is used to find the dimension and degree of such an ideal. The result also suggests that the description of the denominator of an equivariant Hilbert series of an arbitrary ${\textrm {Inc} (\mathbb {N})}$-invariant ideal as given by Nagel and Römer is rather efficient.

Published: 12 March 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2563-2575; https://doi.org/10.1090/proc/13948

Published: 23 October 2017

Proceedings of the American Mathematical Society, Volume 146, pp 845-860; https://doi.org/10.1090/proc/13586

**Abstract:**

In this paper we investigate the relationships between closed AdS -manifolds and Higgs bundles. We have a new way to construct AdS structures that allows us to see many of their properties explicitly, for example we can recover the very recent formula by Tholozan for their volume.

Published: 13 September 2017

Proceedings of the American Mathematical Society, Volume 146, pp 759-771; https://doi.org/10.1090/proc/13855

**Abstract:**

Let $M$ be a 5-dimensional Riemannian manifold with $Sec_M\in [0,1]$ and $\Sigma$ be a locally conformally flat closed hypersurface in $M$ with mean curvature function $H$ . We prove that there exists $\varepsilon _0>0$ such that $\begin{align} \int _\Sigma (1+H^2)^2 \ge \frac {4\pi ^2}{3}\chi (\Sigma ), \end{align}$ provided $\vert H\vert \le \varepsilon _0$ , where $\chi (\Sigma )$ is the Euler number of $\Sigma$ . In particular, if $\Sigma$ is a locally conformally flat minimal hypersphere in $M$ , then $$

Published: 8 January 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2225-2237; https://doi.org/10.1090/proc/13947

**Abstract:**

We study decay of small solutions of the Born-Infeld equation in 1+1 dimensions, a quasilinear scalar field equation modeling nonlinear electromagnetism, as well as branes in String theory and minimal surfaces in Minkowski space-times. From the work of Whitham, it is well known that there is no decay because of arbitrary solutions traveling to the speed of light just as linear wave equation. However, even if there is no global decay in 1+1 dimensions, we are able to show that all globally small H s + 1 × H s H^{s+1}\times H^s , s > 1 2 s>\frac 12 solutions do decay to the zero background state in space, inside a strictly proper subset of the light cone. We prove this result by constructing a Virial identity related to a momentum law, in the spirit of works by Kowalczyk, Martel, and the second author, as well as a Lyapunov functional that controls the H ˙ 1 × L 2 \dot H^1 \times L^2 energy.

Published: 6 October 2017

Proceedings of the American Mathematical Society, Volume 146, pp 1173-1180; https://doi.org/10.1090/proc/13791

**Abstract:**

For a Blaschke product whose zeros lie in a Stolz domain, we find a condition regarding which guarantees that belongs to the Bergman space . In addition, the sharpness of this condition is considered.

Published: 16 February 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2395-2408; https://doi.org/10.1090/proc/13950

Published: 28 September 2017

Proceedings of the American Mathematical Society, Volume 146, pp 1083-1096; https://doi.org/10.1090/proc/13771

**Abstract:**

In this paper, we investigate asymptotic behaviors of Racah polynomials with fixed parameters and scaled variable as the polynomial degree tends to infinity. We start from the difference equation satisfied by the polynomials and derive an asymptotic formula in the outer region via ratio asymptotics. Next, we find the asymptotic formulas in the oscillatory region via a simple matching principle. Unlike the varying parameter case considered in a previous paper, the zeros of Racah polynomials with fixed parameters may not always be real. For this unusual case, we also provide a standard method to determine the oscillatory curve which attracts the zeros of Racah polynomials when the degree becomes large.

Published: 23 October 2017

Proceedings of the American Mathematical Society, Volume 146, pp 939-951; https://doi.org/10.1090/proc/13775

Published: 16 January 2018

Proceedings of the American Mathematical Society, Volume 146, pp 1781-1792; https://doi.org/10.1090/proc/13952

Published: 26 January 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2647-2661; https://doi.org/10.1090/proc/13936

Published: 16 February 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2343-2358; https://doi.org/10.1090/proc/13937

Published: 12 January 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2529-2540; https://doi.org/10.1090/proc/13939

Published: 1 March 2019

Proceedings of the American Mathematical Society, Volume 147, pp 2661-2671; https://doi.org/10.1090/proc/13886

**Abstract:**

We study closed hypersurfaces in an Euclidean space with point singularities. When certain curvature conditions are prescribed on the smooth part of the hypersurface, we study the geometry of image of the normal map.

Published: 1 February 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2195-2205; https://doi.org/10.1090/proc/13938

Published: 14 February 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2623-2635; https://doi.org/10.1090/proc/13935

Published: 9 March 2018

Proceedings of the American Mathematical Society, Volume 146, pp 2523-2528; https://doi.org/10.1090/proc/13931

Published: 1 August 2012

Proceedings of the American Mathematical Society, Volume 140, pp 2671-2686; https://doi.org/10.1090/s0002-9939-2011-11129-8

**Abstract:**

*Central*sets in were introduced by Furstenberg and are known to have substantial combinatorial structure. For example, any central set contains arbitrarily long arithmetic progressions, all finite sums of distinct terms of an infinite sequence, and solutions to all partition regular systems of homogeneous linear equations. We introduce here the notions of

*strongly central*and

*very strongly central*, which as the names suggest are strictly stronger than the notion of central. They are also strictly stronger than

*syndetic*, which in the case of means that gaps are bounded.