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作者：Grove, K; Ziller, W
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作者：Hass, J; Schlafly, R
摘要：The classical isoperimetric inequality in R-3 states that the surface of smallest area enclosing a given volume is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a single circle at an angle of 120 degrees.
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作者：Kozlovski, OS
摘要：In this paper we will show that the assumption on the negative Schwarzian derivative is redundant in the case of C-3 unimodal maps with a nonflat critical point. The following theorem will be proved: For any C-3 unimodal map of an interval with a nonflat critical point there exists an interval around the critical value such that the first entry map to this interval has negative Schwarzian derivative. Another theorem proved in the paper provides useful cross-ratio estimates. Thus, all theorems ...
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作者：Phong, DH; Sturm, J
摘要：A method of algebraic estimates is developed, and used to. study the stability properties of integrals of the form integral (B)/f(z)/(-delta)dV, under small deformations of the function f. The estimates are described in terms of a stratification of the space of functions {R(z) = /P(z)/(E)//Q(z)/(delta)} by algebraic varieties, on each of which the size of the integral of R(z) is given by an explicit algebraic expression. The method gives an independent proof of a result on stability of Tian in...
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作者：Siu, YT
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作者：Moeglin, C
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作者：André, Y
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作者：Ramakrishna, R
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作者：Rudolph, DJ; Weiss, B
摘要：For Gamma a countable amenable group consider those actions of Gamma as measure preserving transformations of a standard probability space, written as (T-gamma)(gamma is an element of Gamma) acting on (X, F, mu). We say (T-gamma)(gamma is an element of Gamma) has completely positive entropy (or simply cpe for short) if for any finite and nontrivial partition P of X the entropy h(T, P) is not zero. Our goal is to demonstrate what. is well known for actions of Z and even Z(d), that actions of co...
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作者：Effros, EG; Junge, M; Ruan, ZJ
摘要：The operator space analogue of the strong form of the principle of local reflexivity is shown to hold for any von Neumann algebra predual, and thus for any C*-algebraic dual. This is in striking contrast to the situation for C*-algebras, since, for example, K(H) does not have that property. The proof uses the Kaplansky density theorem together with a careful analysis of two notions of integrality for mappings of operator spaces.
