Rigidity in the class of orientable compact surfaces of minimal total absolute curvature

Qing Han; Marcus Khuri

doi:10.1016/j.difgeo.2011.04.035

Rigidity in the class of orientable compact surfaces of minimal total absolute curvature

Qing Han
, Marcus Khuri

Mathematics

University of Notre Dame

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

1 Scopus citations

Abstract

Consider an orientable compact surface in three-dimensional Euclidean space with minimum total absolute curvature. If the Gaussian curvature changes sign to finite order and satisfies a nondegeneracy condition along closed asymptotic curves, we show that any other isometric surface differs by at most a Euclidean motion.

Original language	English
Pages (from-to)	463-472
Number of pages	10
Journal	Differential Geometry and its Application
Volume	29
Issue number	4
DOIs	https://doi.org/10.1016/j.difgeo.2011.04.035
State	Published - Aug 2011

Keywords

Asymptotic curve
Rigidity
Tight surface
Total absolute curvature

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10.1016/j.difgeo.2011.04.035

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title = "Rigidity in the class of orientable compact surfaces of minimal total absolute curvature",

abstract = "Consider an orientable compact surface in three-dimensional Euclidean space with minimum total absolute curvature. If the Gaussian curvature changes sign to finite order and satisfies a nondegeneracy condition along closed asymptotic curves, we show that any other isometric surface differs by at most a Euclidean motion.",

keywords = "Asymptotic curve, Rigidity, Tight surface, Total absolute curvature",

author = "Qing Han and Marcus Khuri",

year = "2011",

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language = "English",

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AU - Khuri, Marcus

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AB - Consider an orientable compact surface in three-dimensional Euclidean space with minimum total absolute curvature. If the Gaussian curvature changes sign to finite order and satisfies a nondegeneracy condition along closed asymptotic curves, we show that any other isometric surface differs by at most a Euclidean motion.

KW - Asymptotic curve

KW - Rigidity

KW - Tight surface

KW - Total absolute curvature

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JO - Differential Geometry and its Application

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ER -

Rigidity in the class of orientable compact surfaces of minimal total absolute curvature

Abstract

Keywords

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