f-调和函数的Hess矩阵的估计及其在分裂定理中的应用

Estimates for the Hessian of f-harmonic functions and their applications to splitting theorem

得到了f-调和函数的Hess矩阵的一个新的估计。运用这个新的估计,对具有加权Poincaré不等式以及Bakry-mery Ricci曲率的下界是负函数的光滑度量测度空间上的一个分裂定理进行了改进。

A new estimate for the Hessian of f-harmonic functions is obtained. Using the new estimate, we improve a splitting theorem on smooth metric measure space with weighted Poincar6 inequality under the condition that the Bakry- Emery Ricci curvature is bounded from below by some negative functions.