Hyperbolic geometric flow (I): short-time existence and nonlinear stability

Details Hyperbolic geometric flow (I): short-time existence and nonlinear stability Hyperbolic geometric flow (I): short-time existence and nonlinear stability

2006-10-08

arxiv.org/abs/math/0610256v2

Mathematics

Differential Geometry

Scientific paper

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.

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