Illinois Journal of Mathematics

Metrics of constant curvature 1 with three conical singularities on the $2$-sphere

Masaaki Umehara and Kotaro Yamada

Full-text: Open access

Abstract

A necessary and sufficient condition for the existence and the uniqueness of a conformal metric on a $2$-sphere of constant curvature 1 and with three conical singularities of prescribed order is given.

Article information

Source
Illinois J. Math., Volume 44, Issue 1 (2000), 72-94.

Dates
First available in Project Euclid: 19 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1255984954

Digital Object Identifier
doi:10.1215/ijm/1255984954

Mathematical Reviews number (MathSciNet)
MR1731382

Zentralblatt MATH identifier
0958.30029

Subjects
Primary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
Secondary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]

Citation

Umehara, Masaaki; Yamada, Kotaro. Metrics of constant curvature 1 with three conical singularities on the $2$-sphere. Illinois J. Math. 44 (2000), no. 1, 72--94. doi:10.1215/ijm/1255984954. https://projecteuclid.org/euclid.ijm/1255984954


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