Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
ABP estimate and Log Sobolev inequality
Geometric structures on G2-moduli spaces
Jihye Lee; Title: ABP estimate and Log Sobolev inequality;
Abstract: Recently, Brendle obtained a Michael-Simon type Sobolev inequality of submanifolds in a Riemannian manifold with nonnegative sectional curvature by applying Alexandroff–Bakelman–Pucci(ABP) method to an appropriate Neumann problem. Since Michael-Simon type Sobolev inequalities have a mean curvature term, it could be used when we investigate minimal surfaces. In this talk, we provide an overview of the ABP method on Riemannian manifolds. Then we present our recent work on logarithmic Sobolev inequality under an intermediate Ricci curvature lower bound. We also show the nonexistence of a closed minimal submanifold as a corollary of this theorem. This is a Joint work with Fabio Ricci.
Thibault Langlais; Title: Geometric structures on G2-moduli spaces;
Abstract: We present some new results on the geometry of G2-moduli spaces. If time permits, we also discuss various similarities and differences with Calabi-Yau moduli spaces.
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