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作者：Guo, Yan; Kim, Chanwoo; Tonon, Daniela; Trescases, Ariane
作者单位：Brown University; University of Wisconsin System; University of Wisconsin Madison; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Universite Paris Saclay
摘要：A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the Boltzmann equation in a strictly convex domain with the specular, bounce-back and diffuse boundary condition. With the aid of a distance function toward the grazing set, we construct weighted classical solutions away from the grazing set for all boundary conditi...
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作者：Fresan, Javier
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：At the end of the 1970s, Gross and Deligne conjectured that periods of geometric Hodge structures with multiplication by an abelian number field are products of values of the gamma function at rational arguments, with exponents determined by the Hodge decomposition. We prove an alternating variant of this conjecture for smooth projective varieties acted upon by an automorphism of finite order, thus improving previous results of Maillot and Rossler. The proof relies on a product formula for per...
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作者：Le, Nam Q.; Savin, Ovidiu
作者单位：Indiana University System; Indiana University Bloomington; Columbia University
摘要：We obtain estimates up to the boundary for solutions to degenerate Monge-AmpSre equations of the type det D(2)u = f in Omega, f similar to dist(alpha)(., partial derivative Omega) near partial derivative Omega, alpha > 0. As a consequence we obtain global estimates up to the boundary for the eigenfunctions of the Monge-AmpSre operator on smooth, bounded, uniformly convex domains in R-n.
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作者：Radu, Nicolas
作者单位：Universite Catholique Louvain
摘要：Let T be a locally finite tree all of whose vertices have valency at least 6. We classify, up to isomorphism, the closed subgroups of acting 2-transitively on the set of ends of T and whose local action at each vertex contains the alternating group. The outcome of the classification for a fixed tree T is a countable family of groups, all containing two remarkable subgroups: a simple subgroup of index and (the semiregular analog of) the universal locally alternating group of Burger-Mozes (with ...
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作者：Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim
作者单位：Lund University; California Institute of Technology; California Institute of Technology; University of New Mexico
摘要：We consider Chebyshev polynomials, T-n(z), for infinite, compact sets e subset of R (that is, the monic polynomials minimizing the sup-norm,parallel to T-n parallel to(e), on ). We resolve a 45+ year old conjecture of Widom that for finite gap subsets of R , his conjectured asymptotics (which we call Szego-Widom asymptotics) holds. We also prove the first upper bounds of the form parallel to T-n parallel to(e) <= QC(e)(n) (where C (e) is the logarithmic capacity of e) for a class of e's with a...
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作者：Le Boudec, Adrien
作者单位：Universite Paris Saclay; Universite Catholique Louvain
摘要：A countable group is -simple if its reduced -algebra is simple. It is well-known that -simplicity implies that the amenable radical of the group must be trivial. We show that the converse does not hold by constructing explicit counter-examples. We additionally prove that every countable group embeds into a countable group with trivial amenable radical and that is not C*-simple.
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作者：Balmer, Paul; Sanders, Beren
作者单位：University of California System; University of California Los Angeles; University of Copenhagen
摘要：We study the spectrum of prime ideals in the tensor-triangulated category of compact equivariant spectra over a finite group. We completely describe this spectrum as a set for all finite groups. We also make significant progress in determining its topology and obtain a complete answer for groups of square-free order. For general finite groups, we describe the topology up to an unresolved indeterminacy, which we reduce to the case of p-groups. We then translate the remaining unresolved question...
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作者：Guan, Pengfei; Lu, Siyuan
作者单位：McGill University
摘要：We establish mean curvature estimate for immersed hypersurface with nonnegative extrinsic scalar curvature in Riemannian manifold (Nn+1,(g) over bar )through regularity study of a degenerate fully nonlinear curvature equation in general Riemannian manifold. The estimate has a direct consequence for the Weyl isometric embedding problem of (S-2, g) in 3-dimensional warped product space (N-3,(g) over bar) . We also discuss isometric embedding problem in spaces with horizon in general relativity, ...
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作者：Boutillier, Cedric; de Tiliere, Beatrice; Raschel, Kilian
作者单位：Sorbonne Universite; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); Universite de Tours
摘要：We introduce a one-parameter family of massive Laplacian operators (Delta(m(k)))(k is an element of(0,1)) defined on isoradial graphs, involving elliptic functions. We prove an explicit formula for the inverse of Delta(m(k)) , the massive Green function, which has the remarkable property of only depending on the local geometry of the graph, and compute its asymptotics. We study the corresponding statistical mechanics model of random rooted spanning forests. We prove an explicit local formula f...
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作者：Dyatlov, Semyon; Zworski, Maciej
作者单位：Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley
摘要：We show that the Ruelle zeta function for a negatively curved oriented surface vanishes at zero to the order given by the absolute value of the Euler characteristic. This result was previously known only in constant curvature.
