The Klein, Hilbert and Poincaré metrics of a domain

✍ Scribed by A.F. Beardon

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 88 KB
• Volume: 105
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(99)00012-6

✦ Synopsis

Let D be a bounded strictly convex domain in Euclidean n-space equipped with its Hilbert metric h(x; y). It is shown that as the points x and y of D approach distinct points on the boundary of D, for any a in D the sum h(x; a) + h(a; y) is asymptotic to h(x; y).