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Soft isoperimetric rigidity

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Takashi Shioya
Tohoku University
Don, 2017-09-14 09:30 - 10:30
MPIM Lecture Hall

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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