College of Liberal Arts & Sciences

# Differential Geometry Seminar

Speaker:

Wu Jinyang

Topic:

Inner regularity of viscosity solutions to the sigma-k Yamabe Problem in the negative case for 2k>n.

**Abstract:**

Using Savin's small perturbation argument, we showed that for 2k> n, the viscosity solution to the sigma-k Yamabe Problem on an open subset of R^n in the negative case is smooth on an open set with the set's complement's measure equaling to 0. This result is optimal in the sense that there are known examples of viscosity solution having a singularity set of Hausdorff dimension n-1. We would like to go through the details of our proof in this seminar.

Event Date:

September 19, 2023 - 11:00am to 11:50am

Location:

B13 MLH

Calendar Category:

Seminar

Seminar Category:

Differential Geometry