Hyperbolic geometric flow (I): short-time existence and nonlinear   stability
  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. 
Wen-Rong Dai, De-Xing Kong and Kefeng Liu