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Min-max Theory for Capillary Surfaces by Li, Chao; Zhou, Xin; Zhu, Jonathan J. is a scholarly article available to read on EtoBox.

What is Min-max Theory for Capillary Surfaces about?

We develop a min-max theory for the construction of capillary surfaces in 3-manifolds with smooth boundary. In particular, for a generic set of ambient metrics, we prove the existence of nontrivial, smooth, almost properly embedded surfaces with any given constant mean curvature $c$, and with smooth boundary contacting at any given constant angle $\theta$. Moreover, if $c$ is nonzero and $\theta$ is not $\frac{\pi}{2}$, then our min-max solution always has multiplicity one. We also establish a stable Bernstein theorem for minimal hypersurfaces with certain contact angles in higher dimensions.

Author

Li, Chao; Zhou, Xin; Zhu, Jonathan J.

Published

2021

Language

EN