American Journal of Mathematics最新文献

{"title":"Howe correspondence of unipotent characters for a finite symplectic/even-orthogonal dual pair","authors":"Shu-Yen Pan","doi":"10.1353/ajm.2024.a928326","DOIUrl":"https://doi.org/10.1353/ajm.2024.a928326","url":null,"abstract":"<p><p>abstract:</p><p>In this paper we give a complete and explicit description of the Howe correspondence of unipotent characters for a finite reductive dual pair of a symplectic group and an even orthogonal group in terms of the Lusztig parametrization. That is, the conjecture by Aubert-Michel-Rouquier is confirmed.</p></p>","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"5 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141147530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stable cones in the thin one-phase problem","authors":"Xavier Fernández-Real, Xavier Ros-Oton","doi":"10.1353/ajm.2024.a928321","DOIUrl":"https://doi.org/10.1353/ajm.2024.a928321","url":null,"abstract":"<p><p>abstract:</p><p>The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one-phase free boundary problem.</p><p>The problem of classifying stable (or minimal) homogeneous solutions in dimensions $ngeq3$ is completely open. In this context, axially symmetric solutions are expected to play the same role as Simons' cone in the classical theory of minimal surfaces, but even in this simpler case the problem is open.</p><p>The goal of this paper is twofold. On the one hand, our first main contribution is to find, for the first time, the stability condition for the thin one-phase problem. Quite surprisingly, this requires the use of ``large solutions'' for the fractional Laplacian, which blow up on the free boundary.</p><p>On the other hand, using our new stability condition, we show that any axially symmetric homogeneous stable solution in dimensions $nle 5$ is one-dimensional, emph{independently} of the parameter $sin (0,1)$.</p></p>","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"42 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141147420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Number of solutions to a special type of unit equations in two unknowns","authors":"Takafumi Miyazaki, István Pink","doi":"10.1353/ajm.2024.a923236","DOIUrl":"https://doi.org/10.1353/ajm.2024.a923236","url":null,"abstract":"<p><p>abstract:</p><p>For any fixed relatively prime positive integers $a$, $b$ and $c$ with $min{a,b,c}&gt;1$, we prove that the equation $a^x+b^y=c^z$ has at most two solutions in positive integers $x$, $y$ and $z$, except for one specific case which exactly gives three solutions. Our result is essentially sharp in the sense that there are infinitely many examples allowing the equation to have two solutions in positive integers. From the viewpoint of a well-known generalization of Fermat's equation, it is also regarded as a 3-variable generalization of the celebrated theorem of Bennett [M.~A. Bennett, On some exponential equations of S. S. Pillai, Canad. J. Math. 53 (2001), no.~2, 897--922] which asserts that Pillai's type equation $a^x-b^y=c$ has at most two solutions in positive integers $x$ and $y$ for any fixed positive integers $a$, $b$ and $c$ with $min{a,b}&gt;1$.</p></p>","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"45 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140323891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Random walks on tori and normal numbers in self-similar sets","authors":"Yiftach Dayan, Arijit Ganguly, Barak Weiss","doi":"10.1353/ajm.2024.a923240","DOIUrl":"https://doi.org/10.1353/ajm.2024.a923240","url":null,"abstract":"<p><p>abstract:</p><p>We study random walks on a $d$-dimensional torus by affine expanding maps whose linear parts commute. Assuming an irrationality condition on their translation parts, we prove that the Haar measure is the unique stationary measure. We deduce that if $Ksubsetmathbb{R}^d$ is an attractor of a finite iterated function system of $ngeq 2$ maps of the form $xmapsto D^{-1}x+t_i$ ($i=1,dotsc,n$), where $D$ is an expanding $dtimes d$ integer matrix, and is the same for all the maps, under an irrationality condition on the translation parts $t_i$, almost every point in $K$ (w.r.t. any Bernoulli measure) has an equidistributed orbit under the map $xmapsto Dx$ (multiplication mod $mathbb{Z}^d$). In the one-dimensional case, this conclusion amounts to normality to base $D$. Thus for example, almost every point in an irrational dilation of the middle-thirds Cantor set is normal to base $3$.</p></p>","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"53 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140323849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the σκ-Nirenberg problem","authors":"YanYan Li, Luc Nguyen, Bo Wang","doi":"10.1353/ajm.2024.a917542","DOIUrl":"https://doi.org/10.1353/ajm.2024.a917542","url":null,"abstract":"<p><p>abstract:</p><p>We consider the problem of prescribing the $sigma_k$-curvature on the standard sphere $Bbb{S}^n$ with $ngeq 3$. We prove existence and compactness theorems when $kgeq n/2$. This extends an earlier result of Chang, Han, and Yang for $n=4$ and $k=2$.</p></p>","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"12 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139500292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The density hypothesis for horizontal families of lattices","authors":"Mikołaj Fra̧czyk, Gergely Harcos, Péter Maga, Djordje Milićević","doi":"10.1353/ajm.2024.a917540","DOIUrl":"https://doi.org/10.1353/ajm.2024.a917540","url":null,"abstract":"<p><p>abstract:</p><p>We prove the density hypothesis for wide families of arithmetic orbifolds arising from all division quaternion algebras over all number fields of bounded degree. Our power-saving bounds on the multiplicities of non-tempered representations are uniform in the volume and spectral aspects.</p></p>","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"14 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139500565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The effect of metric behavior at spatial infinity on pointwise wave decay in the asymptotically flat stationary setting","authors":"Katrina Morgan","doi":"10.1353/ajm.2024.a917539","DOIUrl":"https://doi.org/10.1353/ajm.2024.a917539","url":null,"abstract":"<p><p>abstract:</p><p>The current work considers solutions to the wave equation on asymptotically flat, stationary, Lorentzian spacetimes in $(1+3)$ dimensions. We investigate the relationship between the rate at which the geometry tends to flat and the pointwise decay rate of solutions. The case where the spacetime tends toward flat at a rate of $|x|^{-1}$ was studied by Tataru (2013), where a $t^{-3}$ pointwise decay rate was established. Here we extend the result to geometries tending toward flat at a rate of $|x|^{-kappa}$ and establish a pointwise decay rate of $t^{-kappa-2}$ for $kappainBbb{N}$ with $kappage 2$. We assume a weak local energy decay estimate holds, which restricts the geodesic trapping allowed on the underlying geometry. We use the resolvent to connect the time Fourier Transform of a solution to the Cauchy data. Ultimately the rate of pointwise wave decay depends on the low frequency behavior of the resolvent, which is sensitive to the rate at which the background geometry tends to flat.</p></p>","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"35 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139500671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global well-posedness for the radial, defocusing, nonlinear wave equation for 3 < p < 5","authors":"Benjamin Dodson","doi":"10.1353/ajm.2024.a917538","DOIUrl":"https://doi.org/10.1353/ajm.2024.a917538","url":null,"abstract":"<p><p>abstract:</p><p>In this paper we continue the study of the defocusing, energy-subcritical nonlinear wave equation with radial initial data lying in the critical Sobolev space. In this case we prove scattering in the critical norm when $3&lt;p&lt;5$.</p></p>","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"42 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139500690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Inverse problems for real principal type operators","authors":"Lauri Oksanen, Mikko Salo, Plamen Stefanov, Gunther Uhlmann","doi":"10.1353/ajm.2024.a917541","DOIUrl":"https://doi.org/10.1353/ajm.2024.a917541","url":null,"abstract":"<p><p>abstract:</p><p>We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray transforms of lower order coefficients. We also give two different boundary determination methods for general operators, and prove global uniqueness results for determining coefficients in nonlinear real principal type equations. The article presents a unified approach for treating inverse boundary problems for transport and wave equations, and highlights the role of propagation of singularities in the solution of related inverse problems.</p></p>","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"3 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139500388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Index to Volume 145: 2023","authors":"","doi":"10.1353/ajm.2023.a913299","DOIUrl":"https://doi.org/10.1353/ajm.2023.a913299","url":null,"abstract":"&lt;p&gt;AMERICAN JOURNAL OF MATHEMATICS Founded in 1878 by Johns Hopkins University INDEX TO VOLUME 145 2023 PAGE AHLGREN, SCOTT, OLIVIA BECKWITH, and MARTIN RAUM. Scarcity of congruences for the partition function . . . . . . . . . . . . . . . . . . . . . . . . . . 1509 AISTLEITNER, CHRISTOPH, NICLAS TECHNAU, and AGAMEMNON ZAFEIROPOULOS. On the order of magnitude of Sudler products . 721 AN, XINLIANG, HAOYANG CHEN, and SILU YIN. Low regularity illposedness for elastic waves driven by shock formation . . . . . . . . . . . 1111 ASTORG, MATTHIEU and FABRIZIO BIANCHI. Hyperbolicity and bifurcations in holomorphic families of polynomial skew products. . . . . 861 BECKWITH, OLIVIA. See AHLGREN, SCOTT BELLAZZINI, JACOPO and DAVID RUIZ. Finite energy traveling waves for the Gross-Pitaevskii equation in the subsonic regime. . . . . . . . . . 109 BESAU, FLORIAN, THOMAS HACK, PETER PIVOVAROV, and FRANZ E. SCHUSTER. Spherical centroid bodies . . . . . . . . . . . . . . . . . . . . . . . . . . 515 BIANCHI, FABRIZIO. See ASTORG, MATTHIEU BONSANTE, FRANCESCO, GABRIELE MONDELLO, and JEAN-MARC SCHLENKER. Minimizing immersions of a hyperbolic surface in a hyperbolic 3-manifold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 995 BRUCE, CHRIS and XIN LI. On K-theoretic invariants of semigroup C∗-algebras from actions of congruence monoids. . . . . . . . . . . . . . . . 251 BUIUM, ALEXANDRU and LANCE EDWARD MILLER. Perfectoid spaces arising from arithmetic jet spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 BULUT, AYNUR. Blow-up criteria below scaling for defocusing energysupercritical NLS and quantitative global scattering bounds. . . . . . . 543 CANTAT, SERGE, ANDRIY REGETA, and JUNYI XIE. Families of commuting automorphisms, and a characterization of the affine space . 413 CHAN, MELODY, CAREL FABER, SØREN GALATIUS, and SAM PAYNE. The Sn-equivariant top weight Euler characteristic of Mg,n . . . . . . 1549 CHEN, HAOJIE and WEIYI ZHANG. Kodaira dimensions of almost complex manifolds, I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477 CHEN, HAOYANG. See AN, XINLIANG CHEN, SHIH-YU and ATSUSHI ICHINO. On Petersson norms of generic cusp forms and special values of adjoint L-functions for GSp4 . . . . 899 FABER, CAREL. See CHAN, MELODY FAOU, ERWAN and PIERRE RAPHAËL. On weakly turbulent solutions to the perturbed linear harmonic oscillator. . . . . . . . . . . . . . . . . . . . . . . . . 1465 FARAH, LUIZ GUSTAVO, JUSTIN HOLMER, SVETLANA ROUDENKO, and KAI YANG. Asymptotic stability of solitary waves of the 3D quadratic Zakharov-Kuznetsov equation . . . . . . . . . . . . . . . . . . . . . . . . 1695 FELDER, GIOVANNI, DAVID KAZHDAN, and ALEXANDER POLISHCHUK . The moduli space of stable supercurves and its canonical line bundle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1777 FERNÁNDEZ, ISABEL, JOSÉ A. GÁLVEZ, and PABLO MIRA.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"2 2","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}