A Mountain-Pass Theorem for Asymptotically Conical Self-Expanders

Jacob Bernstein; Lu Wang

doi:10.1007/s42543-021-00042-w

Peking Mathematical Journal ›› 2022, Vol. 5 ›› Issue (2) : 213 -278. DOI: 10.1007/s42543-021-00042-w

Original Article

A Mountain-Pass Theorem for Asymptotically Conical Self-Expanders

Jacob Bernstein ¹
, Lu Wang ²^,³^,^b

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Abstract

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.

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Jacob Bernstein, Lu Wang. A Mountain-Pass Theorem for Asymptotically Conical Self-Expanders. Peking Mathematical Journal, 2022, 5(2): 213-278 DOI:10.1007/s42543-021-00042-w