# Min-max theory for capillary surfaces

@inproceedings{Li2021MinmaxTF, title={Min-max theory for capillary surfaces}, author={Chaobo Li and Xin Zhou and Jonathan J. Zhu}, year={2021} }

. 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 θ . Moreover, if c is nonzero and θ is not π 2 , then our min-max solution always has multiplicity one. We also establish a stable Bernstein theorem…

## 4 Citations

### Existence of free boundary disks with constant mean curvature in $\mathbb{R}^3$

- Mathematics
- 2022

. Given a surface Σ in R 3 diﬀeomorphic to S 2 , Struwe [38] proved that for almost every H below the mean curvature of the smallest sphere enclosing Σ, there exists a branched immersed disk which…

### Heintze-Karcher inequality and capillary hypersurfaces in a wedge

- Mathematics
- 2022

. In this paper, we utilize the method of Heintze-Karcher to prove a “best” version of Heintze-Karcher-type inequality for capillary hypersurfaces in the half-space or in a wedge. One of new crucial…

### A MAXIMUM PRINCIPLE FOR CODIMENSION-1 STATIONRY VARIFOLDS UNDER FIXED CONTACT ANGLE CONDITION

- Mathematics
- 2022

. In this note, we establish a boundary maximum principle for codimension-1 stationary varifolds, satisfying a ﬁxed contact angle condition in any Riemannian manifold with smooth boundary. MSC 2020:…

### Min-max construction of minimal surfaces with a fixed angle at the boundary

- Mathematics
- 2021

We prove the existence of minimal surfaces in a bounded convex subset of R M intersecting the boundary of M with a fixed contact angle. The proof is based on a min-max construction in the spirit of…

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