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SPACELIKE CAPILLARY SURFACES IN THE LORENTZ–MINKOWSKI SPACE
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 84 / Issue 3 / December 2011
- Published online by Cambridge University Press:
- 09 August 2011, pp. 362-371
- Print publication:
- December 2011
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- Article
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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 umbilical point, which was developed by Choe [‘Sufficient conditions for constant mean curvature surfaces to be round’, Math. Ann.323(1) (2002), 143–156]. Using the concept of the rotation index at the interior and boundary umbilical points and applying the Poincaré–Hopf index formula, we prove that a compact immersed spacelike disk type capillary surface with less than four vertices in a domain of
bounded by (spacelike or timelike) totally umbilical surfaces is part of a (spacelike) plane or a hyperbolic plane. Moreover, we prove that the only immersed spacelike disk type capillary surface inside a de Sitter surface in is part of (spacelike) plane or a hyperbolic plane.
bounded by (spacelike or timelike) totally umbilical surfaces is part of a (spacelike) plane or a hyperbolic plane. Moreover, we prove that the only immersed spacelike disk type capillary surface inside a de Sitter surface in 