Yi Wang


Johns Hopkins University


Tuesday, October 9, 2018 - 4:00pm to 5:00pm



306 Rowland Hall

We consider $\sigma_k$-curvature equation with $H_k$-curvature condition on a compact manifold with boundary $(X^{n+1}, M^n, g)$. When restricting to the closure of the positive $k$-cone, this is a fully nonlinear elliptic equation with a fully nonlinear Robin-type boundary condition. We prove a general bifurcation theorem in order to study nonuniqueness of solutions when $2k<n+1$. We explicitly give examples of product manifolds with multiple solutions. It is analogous to Schoen’s example for Yamabe problem on $S^1\times S^{n-1}$. This is joint work with Jeffrey Case and Ana Claudia Moreira.