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Speaker:

Florentin Münch
Affiliation:

Universität Potsdam
Date:

Thu, 2017-09-28 15:00 - 15:30
Location:

MPIM Lecture Hall
Parent event:

Metric Measure Spaces and Ricci Curvature Ollivier and Bakry Emery curvature are very similar in spirit, however their defnitions

look completely different. Both curvature notions share the applicability of the maximum

principle yielding semigroup characterizations strong enough to prove spectral gap and

diameter bounds under positive curvature. But only Bakry-Emery curvature allows a

Ledoux approach which guarantees Harnack inequality, Liouville property and Buser in-

equality. We will also discuss exponential modifcations of both curvature notions yielding

Li-Yau inequality in the Bakry-Emery case.

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