The gradient flow of the $L^2$ curvature energy on surfaces
Differential Geometry
2010-08-26 v1 Analysis of PDEs
Abstract
We investigate the gradient flow of the norm of the Riemannian curvature on surfaces. We show long time existence with arbitrary initial data, and exponential convergence of the volume normalized flow to a constant scalar curvature metric when the initial energy is below a constant determined by the Euler characteristic of the underlying surface.
Keywords
Cite
@article{arxiv.1008.4311,
title = {The gradient flow of the $L^2$ curvature energy on surfaces},
author = {Jeffrey Streets},
journal= {arXiv preprint arXiv:1008.4311},
year = {2010}
}