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作者：Birbrair, Lev; Neumann, Walter D.; Pichon, Anne
作者单位：Universidade Federal do Ceara; Columbia University; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We describe a natural decomposition of a normal complex surface singularity (X, 0) into its thick and thin parts. The former is essentially metrically conical, while the latter shrinks rapidly in thickness as it approaches the origin. The thin part is empty if and only if the singularity is metrically conical; the link of the singularity is then Seifert fibered. In general the thin part will not be empty, in which case it always carries essential topology. Our decomposition has some analogy wi...
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作者：Marcut, Ioan
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：We prove a rigidity theorem in Poisson geometry around compact Poisson submanifolds, using the Nash-Moser fast convergence method. In the case of one-point submanifolds (fixed points), this implies a stronger version of Conn's linearization theorem [2], also proving that Conn's theorem is a manifestation of a rigidity phenomenon; similarly, in the case of arbitrary symplectic leaves, it gives a stronger version of the local normal form theorem [7]. We can also use the rigidity theorem to compu...
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作者：Lieb, Elliott H.; Solovej, Jan Philip
作者单位：Princeton University; Princeton University; University of Copenhagen
摘要：Wehrl used Glauber coherent states to define a map from quantum density matrices to classical phase space densities and conjectured that for Glauber coherent states the mininimum classical entropy would occur for density matrices equal to projectors onto coherent states. This was proved by Lieb in 1978 who also extended the conjecture to Bloch SU(2) spin-coherent states for every angular momentum J. This conjecture is proved here. We also recall our 1991 extension of the Wehrl map to a quantum...
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作者：Nazarov, Fedor; Tolsa, Xavier; Volberg, Alexander
作者单位：University System of Ohio; Kent State University; Kent State University Salem; Kent State University Kent; ICREA; Autonomous University of Barcelona; Michigan State University
摘要：We prove that if mu is a d-dimensional Ahlfors-David regular measure in , then the boundedness of the d-dimensional Riesz transform in L (2)(mu) implies that the non-BAUP David-Semmes cells form a Carleson family. Combined with earlier results of David and Semmes, this yields the uniform rectifiability of mu.
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作者：Demailly, Jean-Pierre; Hoang Hiep Pham
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Hanoi National University of Education
摘要：In this note, we prove a sharp lower bound for the log canonical threshold of a plurisubharmonic function with an isolated singularity at 0 in an open subset of . This threshold is defined as the supremum of constants c > 0 such that is integrable on a neighborhood of 0. We relate to the intermediate multiplicity numbers , defined as the Lelong numbers of at 0 (so that in particular ). Our main result is that . This inequality is shown to be sharp; it simultaneously improves the classical resu...
