Prescribed Mean Curvature Min-Max Theory in Some Non-Compact Manifolds

Prescribed Mean Curvature Min-Max Theory in Some Non-Compact Manifolds

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Liam Mazurowski, Cornell University
Fine Hall 314

In-Person Talk 

In this talk, we will discuss a technique for applying one-parameter prescribed mean curvature min-max theory in certain non-compact 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 3-manifold 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.