The ideal boundaries of complete open surfaces
type: Item
instance of: scholarly article
title: The ideal boundaries of complete open surfaces
zbMATH Open document ID: 0703.53040
author: Takashi Shioya
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1991-01-01T00:00:00Z
review text: The ideal boundary with Tits metric of a Hadamard manifold has been defined by Gromov as the set of equivalence classes of rays with respect to the asymptotic relation. Here the non-positivity of the sectional curvature is essential to construct the ideal boundary. Nevertheless, in the present paper, we construct the ideal boundary with Tits metric of a finitely connected, oriented, complete and open surface by a new equivalence relation between rays through the existence of the total curvature of the surface. This ideal boundary has many natural geometric properties analogous to the case of the standard flat cone provided the surface has only one end.
Mathematics Subject Classification ID: 53C23
zbMATH DE Number: 4153385
zbMATH Keywords: ideal boundary
zbMATH Keywords: Tits metric
zbMATH Keywords: Hadamard manifold
zbMATH Keywords: total curvature
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227534
OpenAlex ID: W2067965535
Wikidata QID: Q125585882
cites work: Manifolds of nonpositive curvature
cites work: Q5719717
cites work: Visibility manifolds
cites work: Le problème des isoperimetres sur les surfaces ouvertes à courbure positive
cites work: Geodesic Parallel Coordinates in the Large
cites work: A compactification of a manifold with asymptotically nonnegative curvature
cites work: Q3330071
cites work: Q3719434
cites work: On a relation between total curvature and Tits metric
cites work: A relation between the total curvature and the measure of rays. II
cites work: Busemann functions and total curvature
cites work: The role of total curvature on complete noncompact Riemannian 2- manifolds
cites work: Cut locus and parallel circles of a closed curve on a Riemannian plane admitting total curvature
cites work: Total Curvatures and Minimal Areas of Complete Open Surfaces
cites work: An integral formula for the measure of rays on complete open surfaces
cites work: Mass of rays on complete open surfaces
cites work: Q3473765
cites work: On Asymptotic Behavior of the Mass of Rays
cites work: Q3977566
DOI: 10.2748/TMJ/1178227534
description: scientific article; zbMATH DE number 4153385