Abstract:

In this talk, I will present recent developments on geometric inequalities for submanifolds under various curvature assumptions. I will first review the ABP method and its applications to isoperimetric inequalities and Sobolev inequalities. I then discuss Logarithmic Sobolev inequalities, including a recent result (joint with F. Ricci) under nonnegative intermediate Ricci curvature and Euclidean volume growth. In the second part, I introduce Willmore-type inequalities derived from curvature comparison techniques in the setting of integral Ricci curvature and asymptotic Ricci curvature.

Please email Sergio Zamora ([email protected]) for the zoom link.