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- W4386328674 abstract "Abstract In this paper, we investigate the connection between the index and the geometry and topology of capillary surfaces. We prove an index estimate for compact capillary surfaces immersed in general 3-manifolds with boundary. We also study noncompact capillary surfaces with finite index and show that, under suitable curvature assumptions, such surface is conformally equivalent to a compact Riemann surface with boundary, punctured at finitely many points. We then prove that a weakly stable capillary surface immersed in a half-space of <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msup> <m:mi mathvariant=double-struck>R</m:mi> <m:mn>3</m:mn> </m:msup> </m:math> mathbb{R}^{3} which is minimal or has a contact angle less than or equal to <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>π</m:mi> <m:mo>/</m:mo> <m:mn>2</m:mn> </m:mrow> </m:math> pi/2 must be a half-plane. Using this uniqueness result, we obtain curvature estimates for strongly stable capillary surfaces immersed in a 3-manifold with bounded geometry." @default.
- W4386328674 created "2023-09-01" @default.
- W4386328674 creator A5077895443 @default.
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- W4386328674 date "2023-08-30" @default.
- W4386328674 modified "2023-09-27" @default.
- W4386328674 title "Capillary surfaces: Stability, index and curvature estimates" @default.
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- W4386328674 doi "https://doi.org/10.1515/crelle-2023-0050" @default.
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