Prescribed Mean Curvature MinMax Theory in Some NonCompact Manifolds
Prescribed Mean Curvature MinMax Theory in Some NonCompact Manifolds

Liam Mazurowski, Cornell University
Fine Hall 314
InPerson Talk
In this talk, we will discuss a technique for applying oneparameter prescribed mean curvature minmax theory in certain noncompact manifolds. We give two main applications. First, consider a real valued function h on Euclidean space which is asymptotic to a positive constant at infinity. We show that, under certain additional assumptions on h, there exists a closed hypersurface with mean curvature prescribed by h. Second, let M be an asymptotically flat 3manifold and fix a constant c > 0. We show that, under an additional assumption on M, it is possible to find a closed surface of constant mean curvature c in M.