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.