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作者：Mirek, Mariusz; Stein, Elias M.; Trojan, Bartosz
作者单位：Institute for Advanced Study - USA; University of Wroclaw; Princeton University; Wroclaw University of Science & Technology
摘要：We prove l(p)(Z(d)) bounds for p is an element of(1,infinity) of r-variations r is an element of(2,infinity) for discrete averaging operators and truncated singular integrals of Radon type. We shall present a new powerful method which allows us to deal with these operators in a unified way and obtain the range of parameters of p and r which coincide with the ranges of their continuous counterparts.
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作者：Bertola, Marco; Korotkin, Dmitry; Norton, Chaya
作者单位：Concordia University - Canada; Universite de Montreal; International School for Advanced Studies (SISSA)
摘要：We study the symplectic geometry of the space of linear differential equations with holomorphic coefficients of the form on Riemann surfaces of genus g. This space coincides with the moduli space of projective connections which is an affine bundle modelled on the cotangent bundle . We show that for several choices of the origin, or base, holomorphic projective connection (such as Bergman, Wirtinger or Schottky) the canonical Poisson structure on induces the Goldman bracket on the monodromy cha...
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作者：Tolman, Susan
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：We construct a non-Hamiltonian symplectic circle action on a closed, connected, six-dimensional symplectic manifold with exactly 32 fixed points.
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作者：Liu, Yi
摘要：For an irreducible orientable compact 3-manifold N with empty or incompressible toral boundary, the full -Alexander torsion associated to any real first cohomology class of N is represented by a function of a positive real variable t. The paper shows that is continuous, everywhere positive, and asymptotically monomial in both ends. Moreover, the degree of equals the Thurston norm of . The result confirms a conjecture of J. Dubois, S. Friedl, and W. Luck and addresses a question of W. Li and W....
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作者：Walther, Uli
作者单位：Purdue University System; Purdue University
摘要：For a germ f on a complex manifold X, we introduce a complex derived from the Liouville form acting on logarithmic differential forms, and give an exactness criterion. We use this Liouville complex to connect properties of the D-module generated by to homological data of the Jacobian ideal; specifically we show that for a large class of germs the annihilator of is generated by derivations. Through local cohomology, we connect the cohomology of the Milnor fiber to the Jacobian module via logari...
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作者：Cavalletti, Fabio; Mondino, Andrea
作者单位：University of Pavia; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Zurich
摘要：We prove that if is a metric measure space with having (in a synthetic sense) Ricci curvature bounded from below by and dimension bounded above by , then the classic L,vy-Gromov isoperimetric inequality (together with the recent sharpening counterparts proved in the smooth setting by Milman for any , and upper diameter bounds) holds, i.e. the isoperimetric profile function of is bounded from below by the isoperimetric profile of the model space. Moreover, if equality is attained for some volum...
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作者：Lamel, Bernhard; Mir, Nordine
作者单位：University of Vienna; Qatar Foundation (QF); Texas A&M University Qatar
摘要：It is shown that any formal holomorphic mapping sending a real-analytic generic submanifold M subset of C-N of finite type into a real-analytic strongly pseudoconvex CR submanifold M' subset of C-N' is necessarily convergent. As a consequence, we obtain a positive answer to the long-standing open question of whether formal holomorphic maps sending real-analytic strongly pseudoconvex hypersurfaces into each other are convergent.
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作者：Faure, Frederic; Tsujii, Masato
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Kyushu University
摘要：We consider the semi-classical (or Gutzwiller-Voros) zeta functions for contact Anosov flows. Analyzing the spectra of the generators of some transfer operators associated to the flow, we prove that, for arbitrarily small , its zeros are contained in the union of the -neighborhood of the imaginary axis, , and the half-plane , up to finitely many exceptions, where is the hyperbolicity exponent of the flow. Further we show that the density of the zeros along the imaginary axis satisfy an analogu...
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作者：Hochman, Michael; Solomyak, Boris
作者单位：Hebrew University of Jerusalem
摘要：Let mu be a measure on SL2(R) generating a non-compact and totally irreducible subgroup, and let nu be the associated stationary (Furstenberg) measure for the action on the projective line. We prove that if mu is supported on finitely many matrices with algebraic entries, then dim nu = min {1, h(RW)(mu)/2 chi(mu)} where h(RW)(mu) is the random walk entropy of mu, chi(mu) is the Lyapunov exponent for the random matrix product associated with mu, and dim denotes pointwise dimension. In particula...
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作者：Rajala, Kai
作者单位：University of Jyvaskyla
摘要：We establish uniformization results for metric spaces that are homeomorphic to the Euclidean plane or sphere and have locally finite Hausdorff 2-measure. Applying the geometric definition of quasiconformality, we give a necessary and sufficient condition for such spaces to be QC equivalent to the Euclidean plane, disk, or sphere. Moreover, we show that if such a QC parametrization exists, then the dilatation can be bounded by 2. As an application, we show that the Euclidean upper bound for mea...
