• Corpus ID: 244462934

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… 

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