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arXiv · 2205.12931

The anisotropic Min-Max theory: Existence of anisotropic minimal and CMC surfaces

Guido De Philippis·Antonio De Rosa
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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 [Invent. Math.,1983] in dimension $3$.

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Guido De Philippis, Antonio De Rosa. 2022-05-23. The anisotropic Min-Max theory: Existence of anisotropic minimal and CMC surfaces. https://arxiv.org/abs/2205.12931

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