## Construction of hypersurfaces of prescribed mean curvature

Jonathan Zhu

Harvard University; Visitor, School of Mathematics

October 9, 2018

We'll describe a joint project with X. Zhou in which we use min-max techniques to prove existence of closed hypersurfaces with prescribed mean curvature in closed Riemannian manifolds. Our min-max theory handles the case of nonzero constant mean curvature, and more recently a generic class of smooth prescription functions, without assuming a sign condition.