Explicit construction of extremal Hermitian metrics with finite conical singularities on \(S^2\)
type: Item
instance of: scholarly article
title: Explicit construction of extremal Hermitian metrics with finite conical singularities on \(S^2\)
zbMATH Open document ID: 1021.58008
author: Chang-Shou Lin
author: Xiaohua Zhu
published in: Communications in Analysis and Geometry
publication date: 2003-10-12T00:00:00Z
review text: The authors construct a class of nonradial extremal Hermitian metrics with finite conical singular angles \(2\pi n_i\), \(n_i\) integer, on the sphere. They use ODE methods and the geometry of Gaussian curvature of so-called HCMU metrics, which are the simplest cases of Calabi's extremal metrics in singular spaces. Moreover, the considered HCMU metrics on \(S^2\) are classified: explicit formulae are given via rational holomorphic functions on \(\mathbb{C}\).
reviewed by: Richárd Rimányi
Mathematics Subject Classification ID: 58E11
zbMATH DE Number: 1775022
zbMATH Keywords: extremal Hermitian metrics
zbMATH Keywords: conical singularities
MaRDI profile type: Publication
full work available at URL: cag.2002.v10.n1.a8
OpenAlex ID: W2619558147
DOI: 10.4310/CAG.2002.V10.N1.A8
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description: scientific article; zbMATH DE number 1775022