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作者：Kim, Sang-hyun; Koberda, Thomas
作者单位：Korea Institute for Advanced Study (KIAS); University of Virginia
摘要：Let M be a circle or a compact interval, and let alpha = k + tau >= 1 be a real number such that k = [alpha]. We write Diff(+)(alpha)(M) for the group of orientation preserving C-k diffeomorphisms of M whose kth derivatives are Holder continuous with exponent tau. We prove that there exists a continuum of isomorphism types of finitely generated subgroups G <= Diff(+)(alpha)(M) with the property that G admits no injective homomorphisms into boolean OR(beta>alpha) Diff(+)(beta)(M). We also show ...
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作者：Guth, Larry; Iosevich, Alex; Ou, Yumeng; Wang, Hong
作者单位：Massachusetts Institute of Technology (MIT); University of Rochester; City University of New York (CUNY) System; Baruch College (CUNY)
摘要：If E subset of R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E \subset \mathbb {R}<^>2$$\end{document} is a compact set of Hausdorff dimension greater than 5 / 4, we prove that there is a point x is an element of E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \use...
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作者：Kielak, Dawid
作者单位：University of Bielefeld
摘要：We study the Newton polytopes of determinants of square matrices defined over rings of twisted Laurent polynomials. We prove that such Newton polytopes are single polytopes (rather than formal differences of two polytopes); this result can be seen as analogous to the fact that determinants of matrices over commutative Laurent polynomial rings are themselves polynomials, rather than rational functions. We also exhibit a relationship between the Newton polytopes and invertibility of the matrices...
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作者：Bethuel, Fabrice
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite
摘要：The present paper presents a counterexample to the sequential weak density of smooth maps between two manifolds M and N in the Sobolev space W-1,W-p(M, N), in the case p is an integer. It has been shown (see e.g. Bethuel in Acta Math 167:153-206, 1991) that, if p < dim M is not an integer and the [p]-th homotopy group pi([p])(N) of N is not trivial, [p] denoting the largest integer less then p, then smooth maps are not sequentially weakly dense in W-1,W-p(M, N). On the other hand, in the case ...
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作者：Asok, Aravind; Fasel, Jean; Williams, Ben
作者单位：University of Southern California; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); University of British Columbia
摘要：We show that an old conjecture of A. A. Suslin characterizing the image of a Hurewicz map from Quillen K-theory in degree n to Milnor K-theory in degree n admits an interpretation in terms of unstable A1-homotopy sheaves of the general linear group. Using this identification, we establish Suslin's conjecture in degree 5 for infinite fields having characteristic unequal to 2 or 3. We do this by linking the relevant unstable A1-homotopy sheaf of the general linear group to the stable A1-homotopy...
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作者：Chambers, Gregory R.; Liokumovich, Yevgeny
作者单位：Rice University; Massachusetts Institute of Technology (MIT); University of Toronto
摘要：We prove that every complete non-compact manifold of finite volume contains a (possibly non-compact) minimal hypersurface of finite volume. The main tool is the following result of independent interest: if a region U can be swept out by a family of hypersurfaces of volume at most V, then it can be swept out by a family of mutually disjoint hypersurfaces of volume at most V+epsilon.
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作者：Killip, Rowan; Murphy, Jason; Visan, Monica
作者单位：University of California System; University of California Los Angeles; University of Missouri System; Missouri University of Science & Technology
摘要：We consider the Korteweg-de Vries equation with white noise initial data, posed on the whole real line, and prove the almost sure existence of solutions. Moreover, we show that the solutions obey the group property and follow a white noise law at all times, past or future. As an offshoot of our methods, we also obtain a new proof of the existence of solutions and the invariance of white noise measure in the torus setting.
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作者：Ein, Lawrence; Niu, Wenbo; Park, Jinhyung
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; University of Arkansas System; University of Arkansas Fayetteville; Sogang University
摘要：In recent years, the equations defining secant varieties and their syzygies have attracted considerable attention. The purpose of the present paper is to conduct a thorough study on secant varieties of curves by settling several conjectures and revealing interaction between singularities and syzygies. The main results assert that if the degree of the embedding line bundle of a nonsingular curve of genusgis greater than 2g+2k+p for nonnegative integerskandp, then thek-th secant variety of the c...
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作者：Lawrence, Brian; Venkatesh, Akshay
作者单位：University of Chicago; Institute for Advanced Study - USA
摘要：We give an alternative proof of Faltings's theorem (Mordell's conjecture): a curve of genus at least two over a number field has finitely many rational points. Our argument utilizes the set-up of Faltings's original proof, but is in spirit closer to the methods of Chabauty and Kim: we replace the use of abelian varieties by a more detailed analysis of the variation of p-adic Galois representations in a family of algebraic varieties. The key inputs into this analysis are the comparison theorems...
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作者：Benoist, Olivier; Wittenberg, Olivier
作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：We formulate the real integral Hodge conjecture, a version of the integral Hodge conjecture for real varieties, and raise the question of its validity for cycles of dimension 1 on uniruled and Calabi-Yau threefolds and on rationally connected varieties. We relate it to the problem of determining the image of the Borel-Haefliger cycle class map for 1-cycles, with the problem of deciding whether a real variety with no real point contains a curve of even geometric genus and with the problem of co...
