Min-max construction of anisotropic CMC surfaces

2022.08.25（星期四）21:00-22:00

点：Zoom ID: 924 888 5804  Passcode: AMSS2022

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要：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.