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A compact minimal shadow boundary in Euclidean space is totally geodesic

✍ Scribed by Antonio J. Di Scala, Jesus Jerónimo-Castro, Gabriel Ruiz-Hernández

Book ID
118788506
Publisher
Springer Vienna
Year
2011
Tongue
English
Weight
148 KB
Volume
168
Category
Article
ISSN
0026-9255

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📜 SIMILAR VOLUMES

An estimate on the total curvature of a
An estimate on the total curvature of a geodesic in Euclidean 3-space-with-boundary
✍ 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