TY - JOUR
T1 - Min-max theory for capillary surfaces
AU - Li, Chao
AU - Zhou, Xin
AU - Zhu, Jonathan J.
N1 - Publisher Copyright:
© 2024 the author(s), published by De Gruyter 2025.
PY - 2025/1/1
Y1 - 2025/1/1
N2 - 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, and with smooth boundary contacting at any given constant angle . Moreover, if is nonzero and Θ is not π/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.
AB - 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, and with smooth boundary contacting at any given constant angle . Moreover, if is nonzero and Θ is not π/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.
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U2 - 10.1515/crelle-2024-0075
DO - 10.1515/crelle-2024-0075
M3 - Article
AN - SCOPUS:85208250272
SN - 0075-4102
VL - 2025
SP - 215
EP - 262
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 818
ER -