Rigidity in the Class of Orientable Compact Surfaces of Minimal Total Absolute Curvature

Details Rigidity in the Class of Orientable Compact Surfaces of Minimal Total Absolute Curvature Rigidity in the Class of Orientable Compact Surfaces of Minimal Total Absolute Curvature

2011-04-04

arxiv.org/abs/1104.0474v1

Mathematics

Differential Geometry

Differential Geom. Appl., to appear, 16 pages

Scientific paper

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.

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