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作者：Nonnenmacher, Stephane; Zworski, Maciej
作者单位：Universite Paris Saclay; CEA; Centre National de la Recherche Scientifique (CNRS); University of California System; University of California Berkeley
摘要：We prove that for evolution problems with normally hyperbolic trapping in phase space, correlations decay exponentially in time. Normally hyperbolic trapping means that the trapped set is smooth and symplectic and that the flow is hyperbolic in directions transversal to it. Flows with this structure include contact Anosov flows, classical flows in molecular dynamics, and null geodesic flows for black holes metrics. The decay of correlations is a consequence of the existence of resonance free s...
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作者：Friedlander, J. B.; Iwaniec, H.; Mazur, B.; Rubin, K.
作者单位：University of Toronto; Rutgers University System; Rutgers University New Brunswick; Harvard University; University of California System; University of California Irvine
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作者：Guan, Qi'an; Zhou, Xiangyu
作者单位：Peking University; Peking University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences
摘要：In this article, stimulated by the effectiveness in Berndtsson's solution of the openness conjecture and continuing our solution of Demailly's strong openness conjecture, we discuss conditions to guarantee the effectiveness of the conjecture and establish such an effectiveness result. We explicitly point out a lower semicontinuity property of plurisubharmonic functions with a multiplier, which is implicitly contained in Guan and Zhou (2014, arXiv:1401.7158). We also obtain optimal effectivenes...
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作者：Li, Wen-Wei
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
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作者：Crovisier, Sylvain; Pujals, Enrique R.
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We prove that any diffeomorphism of a compact manifold can be approximated in the topology by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by one which is essentially hyperbolic (has a finite number of transitive hyperbolic attractors with open and dense basin of attraction).
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作者：Andersson, Mats; Wulcan, Elizabeth
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：We prove global effective versions of the Briancon-Skoda-Huneke theorem. Our results extend, to singular varieties, a result of Hickel on the membership problem in polynomial ideals in , and a related theorem of Ein and Lazarsfeld for smooth projective varieties. The proofs rely on known geometric estimates and new results on multivariable residue calculus.
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作者：Liu, Kefeng; Rao, Sheng; Yang, Xiaokui
作者单位：Zhejiang University; University of California System; University of California Los Angeles; Wuhan University; Northwestern University
摘要：We prove several formulas related to Hodge theory and the Kodaira-Spencer-Kuranishi deformation theory of Kahler manifolds. As applications, we present a construction of globally convergent power series of integrable Beltrami differentials on Calabi-Yau manifolds and also a construction of global canonical family of holomorphic -forms on the deformation spaces of Calabi-Yau manifolds. Similar constructions are also applied to the deformation spaces of compact Kahler manifolds.
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作者：Goncharov, Alexander; Shen, Linhui
作者单位：Yale University
摘要：A decorated surface is an oriented surface with boundary and a finite, possibly empty, set of special points on the boundary, considered modulo isotopy. Let be a split reductive group over . A pair gives rise to a moduli space , closely related to the moduli space of -local systems on . It is equipped with a positive structure (Fock and Goncharov, Publ Math IHES 103:1-212, 2006). So a set of its integral tropical points is defined. We introduce a rational positive function on the space , calle...
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作者：McKinnon, David; Roth, Mike
作者单位：University of Waterloo; Queens University - Canada
摘要：In this paper, we associate an invariant to an algebraic point on an algebraic variety with an ample line bundle . The invariant measures how well can be approximated by rational points on , with respect to the height function associated to . We show that this invariant is closely related to the Seshadri constant measuring local positivity of at , and in particular that Roth's theorem on generalizes as an inequality between these two invariants valid for arbitrary projective varieties.
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作者：Cheraghi, Davoud; Cheritat, Arnaud
作者单位：Imperial College London; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Inria
摘要：Marmi, Moussa and Yoccoz conjectured that some error function , related to the approximation of the size of Siegel disks by some arithmetic function of the rotation number , is a Holder continuous function of with exponent . Using the renormalization invariant class of Inou and Shishikura, we prove this conjecture for the restriction of to a class of high type numbers.
