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Rigidity of capillary surfaces in compact 3-manifolds with strictly convex boundary
Published online by Cambridge University Press: 03 April 2023
Abstract
In this paper, we obtain one sharp estimate for the length 
$L(\partial\Sigma)$ of the boundary 
$\partial\Sigma$ of a capillary minimal surface Σ2 in M3, where M is a compact three-manifolds with strictly convex boundary, assuming Σ has index one. The estimate is in term of the genus of Σ, the number of connected components of 
$\partial\Sigma$ and the constant contact angle θ. Making an extra assumption on the geometry of M along 
$\partial M$, we characterize the global geometry of M, which is saturated only by the Euclidean three-balls. For capillary stable CMC surfaces, we also obtain similar results.
Keywords
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- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 66 , Issue 1 , February 2023 , pp. 231 - 240
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.
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