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Speaker:

Takashi Shioya
Affiliation:

Tohoku University
Date:

Thu, 2017-09-14 09:30 - 10:30
Location:

MPIM Lecture Hall
Parent event:

Metric Measure Spaces and Ricci Curvature In this talk, we consider the relation between isoperimetric profile and observable variance, where the observable variance is defined to be the supremum of the variance of 1-Lipschitz functions. We have the detailed metric structure of a metric measure space such that its isoperimetric profile is not greater than that of a one-dimensional model and the observable variance coincides with that of the model. As an application, we obtain a new type of splitting theorem for a complete Riemannian manifold with positive Bakry-Emery Ricci curvature. This is a joint work with Hiroki Nakajima.

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