Curvature flows on four manifolds with boundary
Analysis of PDEs
2007-08-16 v1 Differential Geometry
Abstract
Given a compact four dimensional smooth Riemannian manifold with smooth boundary, we consider the evolution equation by -curvature in the interior keeping the -curvature and the mean curvature to be zero and the evolution equation by -curvature at the boundary with the condition that the -curvature and the mean curvature vanish. Using integral method, we prove global existence and convergence for the -curvature flow (resp -curvature flow) to smooth metric of prescribed -curvature (resp -curvature) under conformally invariant assumptions.
Cite
@article{arxiv.0708.2029,
title = {Curvature flows on four manifolds with boundary},
author = {Cheikh Birahim Ndiaye},
journal= {arXiv preprint arXiv:0708.2029},
year = {2007}
}