Total excess and Tits metric for piecewise Riemannian 2-manifolds
type: Item
instance of: scholarly article
title: Total excess and Tits metric for piecewise Riemannian 2-manifolds
zbMATH Open document ID: 0924.53030
DOI: 10.1016/S0166-8641(98)00077-7
author: Kazuhiro Kawamura
author: Fumiko Ohtsuka
published in: Topology and its Applications
publication date: 1999-11-08T00:00:00Z
review text: This paper studies the total excess \(e(X)\) of a simply-connected nonpositively curved piecewise Riemannian \(2\)-manifold. In the smooth case the total excess is equal to the total curvature. The second author proved in [\textit{F. Ohtsuka}, Bull. Fac. Sci., Ibaraki Univ., Ser. A 20, 5-8 (1988; Zbl 0666.53026)] that \(e(X)=2\pi-2 \text{diam}_{Td}(X(\infty))\) where \(\text{diam}_{Td}(X(\infty))\) is the diameter of the ideal boundary in the Tits metric. This formula is generalized here to the piecewise Riemannian case. It is also proved that the excess is finite iff the Tits metric induces the same topology at \(X(\infty)\) as the cone topology. Finally, it is shown that any decomposition of a circle into points and intervals is realized as the Tits boundary of some simply connected nonpositively curved piecewise Riemannian \(2\)-manifold.
reviewed by: Igor Belegradek
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 57N05
zbMATH DE Number: 1317230
zbMATH Keywords: excess
zbMATH Keywords: ideal boundary
zbMATH Keywords: piecewise Riemannian
Wikidata QID: Q115339612
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1317230