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arXiv · 1010.2810

Spacelike capillary surfaces in the Lorentz-Minkowski space

Juncheol Pyo·Keomkyo Seo
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Abstract

For a compact spacelike constant mean curvature surface with nonempty boundary in the three-dimensional Lorentz-Minkowski space, we introduce a rotation index of the lines of curvature at the boundary umbilic point, which was developed by Choe \cite{Choe}. Using the concept of the rotation index at the interior and boundary umbilic points and applying the Poincaré-Hopf index formula, we prove that a compact immersed spacelike disk type capillary surface with less than $4$ vertices in a domain of $\Bbb L^3$ bounded by (spacelike or timelike) totally umbilic surfaces is part of a (spacelike) plane or a hyperbolic plane. Moreover we prove that the only immersed spacelike disk type capillary surface inside de Sitter surface in $\Bbb L^3$ is part of (spacelike) plane or a hyperbolic plane.

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Juncheol Pyo, Keomkyo Seo. 2010-10-14. Spacelike capillary surfaces in the Lorentz-Minkowski space. https://arxiv.org/abs/1010.2810

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