A mountain-pass theorem for asymptotically conical self-expanders. (English) Zbl 1539.53103
Summary: We develop a min-max theory for asymptotically conical self-expanders of mean curvature flow. In particular, we show that given two distinct strictly stable self-expanders that are asymptotic to the same cone and bound a domain, there exists a new asymptotically conical self-expander trapped between the two.
MSC:
| 53E10 | Flows related to mean curvature |
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
| 35J20 | Variational methods for second-order elliptic equations |
| 35J93 | Quasilinear elliptic equations with mean curvature operator |
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