Analysis and Geometric Analysis Seminar

Antonio De RosaUniversity of Maryland
Min-max construction of anisotropic CMC surfaces

Monday, October 24, 2022 - 2:40pm
Malott 406

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.