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On graphs in Euclidean spaces with minimal total curvature

✍ Scribed by Hirofumi Nagasaka

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
133 KB
Volume
12
Category
Article
ISSN
0926-2245

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✦ Synopsis

In this paper we study the flat maps, that is, the polygonal maps with minimal total curvature, from a finite graph G to a Euclidean space E n that were recently defined and studied by K. Taniyama. We investigate the local behavior of these flat maps. As a consequence we determine the vertex dimension and the curvature dimension, which are invariants of graphs included by flat maps, of complete graphs.

πŸ“œ 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 πŸ“‚ Article πŸ“… 1982 πŸ› Springer 🌐 English βš– 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

On minimal submanifolds in an Euclidean
On minimal submanifolds in an Euclidean space
✍ Qiaoling Wang πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 90 KB

## Abstract The concepts β€œsuper stable” and β€œsuper index” for minimal submanifolds in a Euclidean space are introduced. These concepts coincide with the usual concepts β€œstable” and β€œindex” when the submanifolds have codimension one. We prove that the only complete super stable minimal submanifolds