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

Seong Deog Yang

doi:10.4134/BKMS.b150984

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

Seong Deog Yang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We solve the Björling 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 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.

Original language	English
Pages (from-to)	159-175
Number of pages	17
Journal	Bulletin of the Korean Mathematical Society
Volume	54
Issue number	1
DOIs	https://doi.org/10.4134/BKMS.b150984
Publication status	Published - 2017

Bibliographical note

Funding Information:
The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2014R1A2A2A01003683). The second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827).

Publisher Copyright:
© 2017 Korean Mathematical Society.

Keywords

Björling formula
Constant mean curvature surfaces
De sitter space

ASJC Scopus subject areas

General Mathematics

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10.4134/BKMS.b150984

Cite this

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title = "Bj{\"o}rling formula for mean curvature one surfaces in hyperbolic three-space and in de sitter three-space",

abstract = "We solve the Bj{\"o}rling 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 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.",

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AU - Yang, Seong Deog

N1 - Funding Information: The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2014R1A2A2A01003683). The second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827). Publisher Copyright: © 2017 Korean Mathematical Society.

PY - 2017

Y1 - 2017

N2 - We solve the Björling 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 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.

AB - We solve the Björling 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 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.

KW - Björling formula

KW - Constant mean curvature surfaces

KW - De sitter space

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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