Smoothening cone points with Ricci flow

Abstract

We consider Ricci flow on a closed surface with cone points.The main result is: given a (nonsmooth) cone metric g 0 over a closed surface there is a smooth Ricci flow g(t) defined for (0, T ], with curvature unbounded above, such that g(t) tends to g 0 as t → 0. This result means that Ricci flow provides a way for instantaneously smoothening cone points.We follow the argument of P. Topping in [9] modifying his reasoning for cusps of negative curvature; in that sense we can consider cusps as a limiting zero-angle cone, and we generalize to any angle between 0 and 2π.

Locations

• arXiv (Cornell University) - View - PDF
• Bulletin de la Société mathématique de France - View