Hyperbolic geometric flow (I): short-time existence and nonlinear stability
Differential Geometry
2007-05-23 v2 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
Abstract
In this paper we establish the short-time existence and uniqueness theorem for hyperbolic geometric flow, and prove the nonlinear stability of hyperbolic geometric flow defined on the Euclidean space with dimension larger than 4. Wave equations satisfied by the curvatures are derived. The relation of hypergeometric flow to the Einstein equation and the Ricci flow is discussed.
Keywords
Cite
@article{arxiv.math/0610256,
title = {Hyperbolic geometric flow (I): short-time existence and nonlinear stability},
author = {Wen-Rong Dai and De-Xing Kong and Kefeng Liu},
journal= {arXiv preprint arXiv:math/0610256},
year = {2007}
}