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作者：Astala, K.; Gonzalez, M. J.
作者单位：University of Helsinki; Universidad de Cadiz
摘要：We study the relation between the geometric properties of a quasicircle and the complex dilatation of a quasiconformal mapping that maps the real line onto . Denoting by S the Beurling transform, we characterize Bishop-Jones quasicircles in terms of the boundedness of the operator on a particular weighted space, and chord-arc curves in terms of its invertibility. As an application we recover the boundedness of the Cauchy integral on chord-arc curves.
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作者：Buhovsky, Lev; Opshtein, Emmanuel
作者单位：Tel Aviv University; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS)
摘要：This paper proceeds with the study of the -symplectic geometry of smooth submanifolds, as initiated in HumiliSre et al. (Duke Math J 164(4), 767-799, 2015) and Opshtein (Ann Sci A parts per thousand c Norm Sup,r 42(5), 857-864, 2009), with the main focus on the behaviour of symplectic homeomorphisms with respect to numerical invariants like capacities. Our main result is that a symplectic homeomorphism may preserve and squeeze codimension 4 symplectic submanifolds (-flexibility), while this is...
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作者：Farkas, Gavril; Kemeny, Michael
作者单位：Humboldt University of Berlin
摘要：Using lattice theory on special surfaces, calculations on moduli stacks of pointed curves and Voisin's proof of Green's Conjecture on syzygies of canonical curves, we prove the Prym-Green Conjecture on the naturality of the resolution of a general Prym-canonical curve of odd genus, as well as (many cases of) the Green-Lazarsfeld Secant Conjecture on syzygies of non-special line bundles on general curves.
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作者：Alekseev, Anton; Rossi, Carlo A.; Torossian, Charles; Willwacher, Thomas
作者单位：University of Geneva; Universite Paris Cite; University of Zurich
摘要：We prove the statement/conjecture of M. Kontsevich on the existence of the logarithmic formality morphism . This question was open since 1999, and the main obstacle was the presence of dr / r type singularities near the boundary in the integrals over compactified configuration spaces. The novelty of our approach is the use of local torus actions on configuration spaces of points in the upper half-plane. It gives rise to a version of Stokes' formula for differential forms with singularities at ...
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作者：Davini, Andrea; Fathi, Albert; Iturriaga, Renato; Zavidovique, Maxime
作者单位：Sapienza University Rome; Ecole Normale Superieure de Lyon (ENS de LYON); CIMAT - Centro de Investigacion en Matematicas; Sorbonne Universite
摘要：We consider a continuous coercive Hamiltonian H on the cotangent bundle of the compact connected manifold M which is convex in the momentum. If is the viscosity solution of the discounted equation where c(H) is the critical value, we prove that converges uniformly, as , to a specific solution of the critical equation We characterize in terms of Peierls barrier and projected Mather measures. As a corollary, we infer that the ergodic approximation, as introduced by Lions, Papanicolaou and Varadh...
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作者：Andersson, John
作者单位：Royal Institute of Technology
摘要：We will show optimal regularity for minimizers of the Signorini problem for the Lame system. In particular if u = (u(1), u(2), ..., u(n)) is an element of W-1,W-2(B-1(+) : R-n) minimizes J (u) = integral(B1+) vertical bar del u+del(perpendicular to)vertical bar(2) + lambda div(u)(2) in the convex set K = {u = (u(1), u(2), ... , u(n)) is an element of W-1,W-2 (B-1(+) : R-n); u(n) = 0 on Pi, u = f is an element of C-infinity(partial derivative B-1) on (partial derivative B-1)(+)}, where lambda >...
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作者：de Fernex, Tommaso; Docampo, Roi
作者单位：Utah System of Higher Education; University of Utah; Universidade Federal Fluminense
摘要：Let be an algebraic variety of characteristic zero. Terminal valuations are defined in the sense of the minimal model program, as those valuations given by the exceptional divisors on a minimal model over . We prove that every terminal valuation over is in the image of the Nash map, and thus it corresponds to a maximal family of arcs through the singular locus of . In dimension two, this result gives a new proof of the theorem of Fernandez de Bobadilla and Pe Pereira stating that, for surfaces...
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作者：Shin, Sug Woo; Templier, Nicolas
作者单位：University of California System; University of California Berkeley; Korea Institute for Advanced Study (KIAS); Cornell University
摘要：We consider certain families of automorphic representations over number fields arising from the principle of functoriality of Langlands. Let be a reductive group over a number field which admits discrete series representations at infinity. Let be the associated -group and a continuous homomorphism which is irreducible and does not factor through . The families under consideration consist of discrete automorphic representations of of given weight and level and we let either the weight or the le...
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作者：Dasgupta, Samit
作者单位：University of California System; University of California Santa Cruz
摘要：We prove that the p-adic L-series of the tensor square of a p-ordinary modular form factors as the product of the symmetric square p-adic L-series of the form and a Kubota-Leopoldt p-adic L-series. This establishes a generalization of a conjecture of Citro. Greenberg's exceptional zero conjecture for the adjoint follows as a corollary of our theorem. Our method of proof follows that of Gross, who proved a factorization result for the Katz p-adic L-series associated to the restriction of a Diri...
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作者：Hoering, Andreas; Peternell, Thomas
作者单位：Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS); University of Bayreuth
摘要：Let be a compact Kahler threefold that is not uniruled. We prove that has a minimal model.
