Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 44, Issue 1 (2000), 72-94.
Metrics of constant curvature 1 with three conical singularities on the $2$-sphere
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.
Illinois J. Math., Volume 44, Issue 1 (2000), 72-94.
First available in Project Euclid: 19 October 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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