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Björling formula for mean curvature one surfaces in hyperbolic three-space and in de Sitter three-space

양성덕
대한수학회 (The Korean Mathematical Society)|2017.01|대한수학회보 (Bulletin of the KMS)|제54권 제1호|pp. 159-175

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참고문헌

키워드

de Sitter spaceBjörling formulaconstant mean curvature surfaces
주제분류수학

초록

We solve the Börling problem for constant mean curvature one surfaces in hyperbolic three-space and in de Sitter three-space. That is, we show that for any regular, analytic (and spacelike in the case of de Sitter three-space) curve γ and an analytic (timelike in the case of de Sitter three-space) unit vector field $N$ along and orthogonal to γ, there exists a unique (spacelike in the case of de Sitter three-space) surface of constant mean curvature 1 which contains γ and the unit normal of which on γ is $N$. Some of the consequences are the planar reflection principles, and a classification of rotationally invariant CMC 1 surfaces.

Abstract

We solve the Börling problem for constant mean curvature one surfaces in hyperbolic three-space and in de Sitter three-space. That is, we show that for any regular, analytic (and spacelike in the case of de Sitter three-space) curve γ and an analytic (timelike in the case of de Sitter three-space) unit vector field $N$ along and orthogonal to γ, there exists a unique (spacelike in the case of de Sitter three-space) surface of constant mean curvature 1 which contains γ and the unit normal of which on γ is $N$. Some of the consequences are the planar reflection principles, and a classification of rotationally invariant CMC 1 surfaces.

참고문헌 (31)

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