Generalized surfaces with constant H/K in Euclidean three-space

Young Wook Kim, Sung Eun Koh, Heayong Shin, Seong-Deog Yang

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Surfaces in Euclidean three-space with constant ratio of mean curvature to Gauss curvature arise naturally as the parallel surfaces to minimal surfaces. They might possess singularities which occur naturally as focal points of minimal surfaces. We study geometric properties and the singularities of such surfaces, prove some global results about them, and provide a Björling formula to construct such surfaces with prescribed point or curve singularities.

Original languageEnglish
Pages (from-to)343-361
Number of pages19
JournalManuscripta Mathematica
Volume124
Issue number3
DOIs
Publication statusPublished - 2007 Nov 1

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Euclidean
Minimal surface
Singularity
Gauss Curvature
Mean Curvature
Curve

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Generalized surfaces with constant H/K in Euclidean three-space. / Kim, Young Wook; Koh, Sung Eun; Shin, Heayong; Yang, Seong-Deog.

In: Manuscripta Mathematica, Vol. 124, No. 3, 01.11.2007, p. 343-361.

Research output: Contribution to journalArticle

Kim, Young Wook ; Koh, Sung Eun ; Shin, Heayong ; Yang, Seong-Deog. / Generalized surfaces with constant H/K in Euclidean three-space. In: Manuscripta Mathematica. 2007 ; Vol. 124, No. 3. pp. 343-361.
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