Rigidity in the Class of Orientable Compact Surfaces of Minimal Total Absolute Curvature
Differential Geometry
2014-01-17 v1 Analysis of PDEs
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.
Cite
@article{arxiv.1104.0474,
title = {Rigidity in the Class of Orientable Compact Surfaces of Minimal Total Absolute Curvature},
author = {Qing Han and Marcus Khuri},
journal= {arXiv preprint arXiv:1104.0474},
year = {2014}
}
Comments
Differential Geom. Appl., to appear, 16 pages