The anisotropic min-max theory: Existence of anisotropic minimal and CMC surfaces

Guido De Philippis, Antonio De Rosa

Research output: Contribution to journalArticlepeer-review

Abstract

We prove the existence of nontrivial closed surfaces with constant anisotropic mean curvature with respect to elliptic integrands in closed smooth 3–dimensional Riemannian manifolds. The constructed min-max surfaces are smooth with at most one singular point. The constant anisotropic mean curvature can be fixed to be any real number. In particular, we partially solve a conjecture of Allard in dimension 3.

Original languageEnglish (US)
JournalCommunications on Pure and Applied Mathematics
DOIs
StateAccepted/In press - 2023

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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