Oberseminar Differentialgeometrie: Jason Ledwidge (Tübingen): The structure of non-compact shrinking Ricci solitons via heat kernel estimates

Montag, 27.01.2020 16:15 im Raum SR4
Mathematik und Informatik

Ricci solitons are solutions to the Ricci flow modulo a diffeomorphism, and arise as singularity models for the Ricci flow. In this talk, we will outline the proof of the uniqueness of the conjugate heat kernel on non-compact shrinking Ricci solitons, without any a priori curvature or volume assumptions. We then use the uniqueness of the conjugate heat kernel to prove that Perelman's celebrated Entropy functional has a unique minimiser on shrinking Ricci solitons. Consequently, this shows that the Riemann tensor is bounded with quadratic decay and that the injectivity radius is bounded from below. These geometric conditions imply shrinking solitons have a unique tangent cone at infinity.

Angelegt am Dienstag, 07.01.2020 10:14 von shupp_01
Geändert am Montag, 20.01.2020 08:57 von shupp_01
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