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On bounds for total absolute curvature of surfaces in hyperbolic 3-space

✍ Scribed by Rémi Langevin; Gil Solanes


Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
98 KB
Volume
336
Category
Article
ISSN
1631-073X

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✦ Synopsis


We construct examples of surfaces in hyperbolic space which do not satisfy the Chern-Lashof inequality (which holds for immersed surfaces in Euclidean space).


📜 SIMILAR VOLUMES


An estimate on the total curvature of a
✍ I. D. Berg 📂 Article 📅 1982 🏛 Springer 🌐 English ⚖ 321 KB

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