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Volume Entropy and the shape of balls in SOL Geometry
时间  Datetime
2019-05-29 14:00 — 15:00 
地点  Venue
Middle Lecture Room(703)
报告人  Speaker
Marc Troyanov
单位  Affiliation
Swiss Federal Institute of Technology (EPFL)
邀请人  Host
Miaomiao Zhu
报告摘要  Abstract

The volume entropy of a complete Riemannian manifold (M, g) is defined as Ent(M, g) = limr→∞ 1 r log Vol(B(x, r)) It has been proved by Ledrappier and Wang that for a compact n-dimensional Riemannian manifold (N, g) with Ricci curvature ≥ −(n−1), we have Ent(M, g) ≤ (n − 1) where M = N˜ is the universal cover of M. With equality if and only if N is a hyperbolic manifold. In this talk, we will compute the volume entropy of SOL, which is a unimodular solvable 3-dimensional Lie group and one of the eight Thurston’s homogenous geometries. This computation requires a fine description of large balls in SOL, which is obtained using an auxiliary Finsler metric.