关于一个Calabi-型曲率流的局部存在性

On the Local Existence of One Calabi-Type Curvature Flow

基于文[14]的讨论,本文将针对一个紧致无边黎曼流形上关于Ricci曲率的L^2-模的负梯度流这一4阶退化抛物型方程组,首先给出其解的局部存在性的详细证明,其次,将在文[14]结果的基础上,进一步在关于此流的奇异性方面讨论解的另一类爆破性态．

As a subsequent paper of [14], the author mainly discusses here the details about the local existence of one negative gradient flow for one L^2-integral of Ricci curvature on any compact manifold, which is actually one fourth order degenerate parabolic equation. Meanwhile, the further discussions about the phenomenon of blowing up for the singularities of the flow are given, according to the earlier results in [14].