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
In-Person Talk听
In this talk, we will discuss a technique for applying one-parameter prescribed mean curvature min-max theory in certain non-compact manifolds.听 We give two main applications.听 First, consider a real valued function h on Euclidean space which is asymptotic to a positive constant at infinity.听 We show that, under certain additional assumptions on h, there exists a closed hypersurface with mean curvature prescribed by h.听 Second, let M be an asymptotically flat 3-manifold and fix a constant c > 0.听 We show that, under an additional assumption on M, it is possible to find a closed surface of constant mean curvature c in M.听
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