Riemann曲面上耗散双曲几何流的整体经典解

Global Classical Solutions to the Dissipative Hyperbolic Geometric Flow on Riemann Surfaces

基于Einstein方程和Hamilton Ricci流为背景,孔德兴和刘克峰最近提出了耗散双曲几何流的概念.考虑耗散双曲几何流Cauchy问题,证明了对于任意给定的初始度量,总存在初始的对称张量,使得经典解整体存在,并且对应的曲率保持一致有界.否则,其经典解会在有限时间内破裂.

The author considers the Cauchy problem for dissipative hyperbolic geometric flow equations introduced recently by Kong D. X. and Liu K. F. motivated by Einstein equation and Hamilton Ricci flow. For the dissipation flow and any given initial metric on in certain class of metrics, it is proved that one can always choose suitable initial velocity symmetric tensor such that the classical global exists for t ≥ 0, and the scalar curvature R（x, t） corresponding to the solution metric gij （x, t） remains uniformly bounded. Otherwise, the solution will blow up at a finite time.