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

Guido De Philippis; Antonio De Rosa

doi:10.1002/cpa.22189

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

Guido De Philippis, Antonio De Rosa

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove the existence of nontrivial closed surfaces with constant anisotropic mean curvature with respect to elliptic integrands in closed smooth (Formula presented.) –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 (Formula presented.).

Original language	English (US)
Pages (from-to)	3184-3226
Number of pages	43
Journal	Communications on Pure and Applied Mathematics
Volume	77
Issue number	7
DOIs	https://doi.org/10.1002/cpa.22189
State	Published - Jul 2024

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1002/cpa.22189

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title = "The anisotropic min-max theory: Existence of anisotropic minimal and CMC surfaces",

abstract = "We prove the existence of nontrivial closed surfaces with constant anisotropic mean curvature with respect to elliptic integrands in closed smooth (Formula presented.) –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 (Formula presented.).",

author = "{De Philippis}, Guido and {De Rosa}, Antonio",

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

Abstract

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