The existence of G-invariant constant mean curvature hypersurfaces

Speaker: Zhiang Wu, Peking University

Title:The existence of G-invariant constant mean curvature hypersurfaces

Time & Venue: 2022.5.27  14:00-14:50  Tencent Meeting：567-833-801

Abstract:In this talk, we consider a closed Riemannian manifold M^n+1 with dimension 3≤n+1≤7, and a compact Lie group G acting as isometries on M with cohomogeneity at least 3. Suppose the union of non-principal orbits M\M^reg is a smooth embedded submanifold of M with dimension at most n？2. Then for any c\in R, we show the existence of a nontrivial, smooth, closed, almost embedded, G-invariant hypersurface Σ^n of constant mean curvature c.