##### Department of Mathematics,

University of California San Diego

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### Math 258-Differential Geometry

## Antonio De Rosa

#### Maryland

## Min-max construction of anisotropic CMC surfaces

##### 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.

### February 9, 2023

### 11:00 AM

APM 7321

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