Mixed initial boundary value problem for hyperbolic geometric flow on Riemann surfaces |
| |
Authors: | Fagui Liu |
| |
Institution: | North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450011, PR China |
| |
Abstract: | The hyperbolic geometric flow equations is introduced recently by Kong and Liu motivated by Einstein equation and Hamilton Ricci flow. In this paper, we consider the mixed initial boundary value problem for hyperbolic geometric flow, and prove the global existence of classical solutions. The results show that, for any given initial metric on R2 in certain class of metric, one can always choose suitable initial velocity symmetric tensor such that the solutions exist, and the scalar curvature corresponding to the solution metric gij keeps bounded. If the initial velocity tensor does not satisfy the certain conditions, the solutions will blow up at a finite time. Some special explicit solutions to the reduced equation are given. |
| |
Keywords: | Hyperbolic geometric flow Mixed initial boundary value problem Riemann surface Classical solution |
本文献已被 ScienceDirect 等数据库收录! |
|