Multiplicity one for min–max theory in compact manifolds with boundary and its applications

Sun, Ao; Wang, Zhichao; Zhou, Xin

doi:10.1007/s00526-024-02669-w

Calc. Var.

2024

DOI: 10.1007/s00526-024-02669-w

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Multiplicity one for min–max theory in compact manifolds with boundary and its applications

Ao Sun,

Zhichao Wang,

Xin Zhou

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2024

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Min-max theory for capillary surfaces

Li,

Zhou,

Zhu

2024

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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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 \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.

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Min-max theory for capillary surfaces

Li,

Zhou,

Zhu

2024

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

View full text Add to dashboard Cite

show abstract

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Multiplicity one for min–max theory in compact manifolds with boundary and its applications

Cited by 1 publication

References 51 publications

Min-max theory for capillary surfaces

Min-max theory for capillary surfaces

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