Distance functions and statistics

✍ Scribed by Jens Chr. Larsen

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 96 KB
• Volume: 45
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(00)00072-3

✦ Synopsis

This paper proves that the Riemannian distance function is maximal in the class of distance functions associated with the Riemannian metric tensor.

Secondly, it is proven that there exists a unique minimum of

on a complete Riemannian surface (M, g) with small curvature, small curvature change and injectivity radius +∞. Here p i ∈ M and γ v is the maximal geodesic with initial velocity v and 0 < t 1 < • • • < t m .