Liouville equation and spherical convex polytopes
HTML articles powered by AMS MathViewer
- by Feng Luo and Gang Tian
- Proc. Amer. Math. Soc. 116 (1992), 1119-1129
- DOI: https://doi.org/10.1090/S0002-9939-1992-1137227-5
- PDF | Request permission
Abstract:
We study the Liouville equation $\Delta u = - {e^{2u}}$ in the complex plane with prescribed singularities and obtain a necessary and sufficient condition for the existence of the solution. The proof is based on the continuity method and a uniqueness theorem.References
- Herbert Busemann, Convex surfaces, Interscience Tracts in Pure and Applied Mathematics, no. 6, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. MR 0105155
- D. Hulin and M. Troyanov, Prescribing curvature on open surfaces, Math. Ann. 293 (1992), no. 2, 277–315. MR 1166122, DOI 10.1007/BF01444716
- Robert C. McOwen, Point singularities and conformal metrics on Riemann surfaces, Proc. Amer. Math. Soc. 103 (1988), no. 1, 222–224. MR 938672, DOI 10.1090/S0002-9939-1988-0938672-X
- Patrick J. Ryan, Euclidean and non-Euclidean geometry, Cambridge University Press, Cambridge, 1986. An analytical approach. MR 854104, DOI 10.1017/CBO9780511806209 W. Thurston, Shape of polyhedrons, preprint.
Bibliographic Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 1119-1129
- MSC: Primary 53C21; Secondary 52A55
- DOI: https://doi.org/10.1090/S0002-9939-1992-1137227-5
- MathSciNet review: 1137227