Minimisation of the Willmore functional under isoperimetric constraint
Tuesday, 26.1.21, 10:00-11:00, virtueller Raum vWang
A Local Singularity Analysis for the Ricci flow
Tuesday, 26.1.21, 11:30-12:30, virtueller Raum vWang
In this talk, I will describe a refined local singularity analysis for the Ricci flow developed jointly with R. Buzano. The key idea is to investigate blow-up rates of the curvature tensor locally, near a singular point. Then I will show applications of this theory to Ricci flows with scalar curvature bounded up to the singular time.
Prescribed curvature measure problem in hyperbolic space
Tuesday, 26.1.21, 15:00-16:00, virtueller Raum vWang
The problem of the prescribed curvature measure is one of the important problems in differential geometry and nonlinear partial differential equations. In this talk, we are going to talk about our recent result about prescribed curvature measure problem in hyperbolic space.We obtained the existence of star-shaped k-convex bodies with prescribed (n-k)-th curvature measures (k<n) by establishing crucial C^2 regularity estimates for solutions to the corresponding fully nonlinear PDE in the hyperbolic space.
Mobius Invariant Equations in Dimension Two
Tuesday, 26.1.21, 16:30-17:30, virtueller Raum vWang
Conformally invariant equations in \(n\bgeq3\) have played an important role in the study of \(\bsigma_k\)-Yamabe problem in geometric analysis. \nIn this talk, we will discuss a class of Mobius invariant equations in dimension two. We will then present related properties for such equations, including Liouville type theorems, Bocher type theorems and existence of solutions. This is a joint work with Yanyan Li and Siyuan Lu.\n