Titlebook: Geometry, Analysis and Probability; In Honor of Jean-Mic Jean-Benoît Bost,Helmut Hofer,Weiping Zhang Book 2017 Springer International Publi

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,Teichmüller Theory for Conic Surfaces,This paper develops the local deformation theory, and some aspects of the global Teichmüller theory, of constant curvature metrics on a surface Σ with a finite number of conic singularities, with all cone angles less than 2.. We approach this using techniques of geometric analysis and the theory of elliptic operators on conic spaces.

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Log-correlated Gaussian Fields: An Overview,We survey the properties of the log-correlated Gaussian field (LGF), which is a centered Gaussian random distribution (generalized function) . on ℝ., defined up to a global additive constant.

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K-stability Implies CM-stability,In this paper, we prove in details that any polarized K-stable manifold is CM-stable. This extends what I did for Fano manifolds in my 2012 paper. Our proof is based on an asymptotic formula for the K-energy and S. Paul’s works ([Pa08], [Pa12], [Pa13]) on the K-stability in terms of stable pairs.

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Jean-Benoît Bost,Helmut Hofer,Weiping ZhangContains contributions by some of the foremost experts in probability and geometry.Explains the most recent advances in these subjects with very careful writing.Provides original research articles of

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https://doi.org/10.1007/978-3-662-66558-9d trace of heat operators. We use the Selberg trace formula to study the asymptotic behavior of the regularized trace for small time. The main result of the paper is a new approach to deal with the weighted orbital integrals on the geometric side of the trace formula.

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On the Analytic Torsion of Hyperbolic Manifolds of Finite Volume,d trace of heat operators. We use the Selberg trace formula to study the asymptotic behavior of the regularized trace for small time. The main result of the paper is a new approach to deal with the weighted orbital integrals on the geometric side of the trace formula.

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