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On the Total Curvature of Immersed Manifolds, I: An Inequality of Fenchel-Borsuk-Willmore

โœ Scribed by Bang-Yen Chen


Book ID
111930667
Publisher
John Hopkins University Press
Year
1971
Tongue
English
Weight
804 KB
Volume
93
Category
Article
ISSN
0002-9327

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In this note we show that the total curvature of a geodesic in the manifoldwith-boundary consisting of Euclidean 3-space with a boundary of the form z = f(x, y) has a bound of at most 2p iff satisfies a Lipschitz condition with the Lipschitz constant at most p. This global result immediately yields