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作者：Ifrim, Mihaela; Tataru, Daniel
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Berkeley
摘要：The first target of this article is the local well-posedness question for 1D quasilinear Schr & ouml;dinger equations with cubic nonlinearities. The study of this class of problems, in all dimensions, was initiated in pioneering work of Kenig-Ponce-Vega for localized initial data, and then continued by Marzuola-Metcalfe-Tataru for initial data in Sobolev spaces. Our objective here is to fully redevelop the study of this problem in the 1D case, and to prove a sharp local well-posedness result. ...
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作者：Wang, Hong; Zahl, Joshua
作者单位：New York University; University of British Columbia
摘要：This paper studies the structure of Kakeya sets in R-3. We show that for every Kakeya set K subset of R-3, there exist well-separated scales 0 < delta < rho <= 1 so that the delta neighborhood of K is almost as large as the rho neighborhood of K. As a consequence, every Kakeya set in R-3 has Assouad dimension 3 and every Ahlfors-David regular Kakeya set in R-3 has Hausdorff dimension 3. We also show that every Kakeya set in R-3 that has stably equal Hausdorff and packing dimension (this is a n...
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作者：Cohen, Alex; Pohoata, Cosmin; Zakharov, Dmitrii
作者单位：Massachusetts Institute of Technology (MIT); Emory University
摘要：Let p1,& mldr;,pn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p_{1},\ldots ,p_{n}$\end{document} be a set of points in the unit square and let T1,& mldr;,Tn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \...
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作者：Becker, Lars; Klein, Ohad; Slote, Joseph; Volberg, Alexander; Zhang, Haonan
作者单位：University of Bonn; Hebrew University of Jerusalem; California Institute of Technology; Michigan State University; University of Bonn; University of South Carolina System; University of South Carolina Columbia
摘要：Let f\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$f$\end{document} be an analytic polynomial of degree at most K-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemar...
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作者：Milman, Emanuel; Shabelman, Shahar; Yehudayoff, Amir
作者单位：Technion Israel Institute of Technology; University of Copenhagen
摘要：The intersection body I K of a star body K in R-n was introduced by E. Lutwak following the work of H. Busemann, and plays a central role in the dual Brunn-Minkowski theory. We show that when n >= 3, (IK)-K-2=cK iff K is a centered ellipsoid, and hence I K = c K iff K is a centered Euclidean ball, answering long-standing questions by Lutwak, Gardner, and Fish-Nazarov-Ryabogin-Zvavitch. An equivalent formulation of the latter in terms of non-linear harmonic analysis states that a non-negative r...
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作者：Alon, Lior; Kummer, Mario; Kurasov, Pavel; Vinzant, Cynthia
作者单位：Massachusetts Institute of Technology (MIT); Technische Universitat Dresden; Stockholm University; University of Washington; University of Washington Seattle
摘要：In this paper, we construct Fourier quasicrystals with unit masses in arbitrary dimensions. This generalizes a one-dimensional construction of Kurasov and Sarnak. To do this, we employ a class of complex algebraic varieties avoiding certain regions in Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathbb{C}}<^>...
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作者：Aggarwal, Amol; Huang, Jiaoyang
作者单位：Columbia University; University of Pennsylvania
摘要：In this paper we show that a Brownian Gibbsian line ensemble whose top curve approximates a parabola must be given by the parabolic Airy line ensemble. More specifically, we prove that if l = (L-1, L-2, ...) is a line ensemble satisfying the Brownian Gibbs property, such that for any epsilon > 0 there exists a constant R (epsilon) > 0 with P[|L-1(t) + 2(-1/2)t(2)|<= epsilon t(2) + R(epsilon)] >= 1-epsilon, for all t is an element of R, then L is the parabolic Airy line ensemble, up to an indep...
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作者：Kra, Bryna; Moreira, Joel; Richter, Florian K.; Robertson, Donald
作者单位：Northwestern University; University of Warwick; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Manchester
摘要：For any set A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A$\end{document} of natural numbers with positive upper Banach density and any k >= 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{up...
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作者：Chen, Shibing; Liu, Jiakun
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS; University of Sydney
摘要：In this paper, we establish a regularity theory for the optimal transport problem when the target is composed of two disjoint convex domains. This is an important model in which singularities arise. Even though the singular set does not exhibit any form of convexity a priori, we prove its higher order regularity by developing novel methods, which also have many other applications. Notably, our results are achieved without requiring any convexity of the source domain. This aligns with Caffarell...
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作者：Regeta, Andriy; Urech, Christian; van Santen, Immanuel
作者单位：University of Padua; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Basel
摘要：Let X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$X$\end{document} be an irreducible variety and Bir(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
