Systols of singular plane surfaces of genus two
type: Item
instance of: scholarly article
title: Systols of singular plane surfaces of genus two
zbMATH Open document ID: 1074.53034
author: Stéphane Sabourau
published in: Mathematische Zeitschrift
publication date: 2005-02-11T00:00:00Z
review text: Given a closed non-simply-connected two-manifold \(M\) with a metric \(g\), we denote by \(\text{sys}(M,g)\) the length of the shortest noncontractible closed geodesic and call \(\sigma(M,g) = \frac{\text{area}(M)}{\text{sys}(M,g)}\) the systolic constant of the metric. A metric is called extremal if it is a local minimum of the functional \(\sigma(M,g)\). The infimum of \(\sigma(M,g)\) taken over all metrics is positive. Calabi conjectured that certain flat metrics with conical singularities on oriented surfaces of genus \(2\) and \(3\) are extremal. The author proves that no flat metric with conical singularities on an oriented closed surface of genus two is extremal.
reviewed by: I. A. Taimanov
Mathematics Subject Classification ID: 53C23
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 2133502
zbMATH Keywords: systoles
zbMATH Keywords: flat metrics with conical singularities
MaRDI profile type: Publication
full work available at URL: s00209-003-0641-9
OpenAlex ID: W2165163722
DOI: 10.1007/S00209-003-0641-9
description: scientific article; zbMATH DE number 2133502