[CvGmt News] Seminario di Esther Cabezas-Rivas (13 feb 2018)
Alfonso Sorrentino
sorrentino at mat.uniroma2.it
Wed Feb 7 15:27:51 CET 2018
SEMINARIO DI EQUAZIONI DIFFERENZIALI
Dipartimento di Matematica
Universita' degli Studi di Roma "Tor Vergata"
Martedi' 13 febbraio 2018, ore 14:30 Aula Dal Passo
Esther Cabezas-Rivas (Goethe-Universität Frankfurt)
Titolo: Ricci flow beyond non-negative curvature conditions
Abstract: We generalize most of the known Ricci flow invariant
non-negative curvature
conditions to less restrictive negative bounds that remain sufficiently
controlled for a short time.
As an illustration of the contents of the talk, we prove that metrics whose
curvature operator has eigenvalues greater than -1 can be evolved by the
Ricci flow for some uniform time such that the eigenvalues of the curvature
operator remain greater than -C. Here the time of existence and the
constant C only depend on the dimension and the degree of
non-collapsedness. We obtain similar generalizations for other invariant
curvature conditions, including positive biholomorphic curvature in the
Kaehler case. We also get a local version of the main theorem.
As an application of our almost preservation results we deduce a variety of
gap and smoothing results of independent interest, including a
classification for non-collapsed manifolds with almost non-negative
curvature operator and a smoothing result for singular spaces coming from
sequences of manifolds with lower curvature bounds. We also obtain a
short-time existence result for the Ricci flow on open manifolds with
almost non-negative curvature (without requiring upper curvature bounds).
This is a joint work with Richard Bamler (Berkeley) and Burkhard Wilking
(Muenster).
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