Uniformization of $S^2$ and flat singular surfaces
Abstract
We construct flat metrics in a given conformal class with prescribed singularities of real orders at marked points of a closed real surface. The singularities can be small conical, cylindrical, and large conical with possible translation component. Along these lines we give an elementary proof of the uniformization theorem for the sphere.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2011
- DOI:
- 10.48550/arXiv.1101.2355
- arXiv:
- arXiv:1101.2355
- Bibcode:
- 2011arXiv1101.2355M
- Keywords:
-
- Mathematics - Differential Geometry;
- Mathematics - Analysis of PDEs;
- 58J60
- E-Print:
- 9 pages