凸流形上的等周界
Isoperimetric Bounds on Convex Manifolds
摘要：
本文将Bobkov和Kannan-Lovász-Simonovits关于欧几里得空间中凸集的Cheeger型等周界推广到具有非负里奇曲率的黎曼流形。为了扩展Bobkov的界，我们需要另外的上界的截面曲率的空间，这使我们能够使用比较工具在Cartan-Alexandrov-Toponogov（或CAT）空间。一路上，我们还定量地改善我们以前的结果，弱浓度的假设意味着一个Cheeger型等周界，一个尖锐的约束相对于所有参数。
英文摘要：
We extend several Cheeger-type isoperimetric bounds for convex sets in Euclidean space, due to Bobkov and Kannan-Lovász-Simonovits, to Riemannian manifolds having non-negative Ricci curvature. In order to extend Bobkov's bound, we require in addition an upper bound on the sectional curvature of the space, which permits us to use comparison tools in Cartan-Alexandrov-Toponogov (or CAT) spaces. Along the way, we also quantitatively improve our previous result that weak concentration assumptions imply a Cheeger-type isoperimetric bound, to a sharp bound with respect to all parameters.
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