Isolated singularities of flat metrics on Riemann surfaces
Differential Geometry
2019-08-15 v1
Abstract
Robert Bryant (Theorie des varietes minimales et applications, 1988, 154: 321-347) proved that an isolated singularity of a conformal metric of positive constant curvature on a Riemann surface is a conical one. Using Complex Analysis, we find all of the local models for an isolated singularity of a flat metric whose area satisfies some polynomial growth condition near the singularity. In particular, we show that an isolated singularity of a flat metric with finite area is also a conical one.
Keywords
Cite
@article{arxiv.1908.04989,
title = {Isolated singularities of flat metrics on Riemann surfaces},
author = {Jin Li and Bin Xu},
journal= {arXiv preprint arXiv:1908.04989},
year = {2019}
}