On a parabolic curvature lower bound generalizing Ricci flows

Prelegent(ci)

Erik Hupp (University of Vienna)

Język referatu

angielski

Termin

5 listopada 2026 12:30

Pokój

p. 5070

Seminarium

Seminarium Zakładu Równań Fizyki Matematycznej

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This talk investigates a connection between two objects of central interest in geometric analysis: (1) Ricci flows (introduced and developed by Hamilton, with powerful analytic tools established later by Perelman); (2) metric-measure spaces satisfying a synthetic curvature lower bound (in the Bochner inequality sense of Bakry-Émery, or the optimal transport sense of Sturm/Lott-Villani). A lesson from (2) is that “good analysis” on a large class of metric-measure spaces, including smooth complete Riemannian manifolds, is ultimately due to a uniform lower bound on the Ricci curvature, suitably generalized. Where, then, is the Ricci lower bound underlying (1)? We will recall Buzano’s “D condition”, and then argue that it is precisely the missing piece. Everything discussed is joint work with M. Flaim.

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