完备黎曼流形上f指数调和型函数的梯度估计（英文）

Gradient estimates for f-exponentially harmonic functions on complete Riemannian manifolds

对于光滑的度量测度空间(M,g,e-fdvol),通过使用极大值原理,考虑了f指数调和型函数的梯度估计.当Bakry-Emery Ricci张量非负并且截面曲率有负下界,可以得到刘维尔型定理.当f为常数时,即为文献[Wu J,Ruan Q,Yang Y H.Gradient estimate for exponentially harmonic functions on complete Riemannian manifolds.Manuscripta Mathematica,2014,143(3-4):483-489]中的结果.

For smooth metric measure spaces(M,g,e-fdvol),the gradient estimates of positive solutions to the f-exponentially harmonic functions was considered by using the maximum principle.Then a Liouville type theorem was obtained when the Bakry-Emery Ricci tensor was nonnegtive and the sectional curvature was bounded by a negative constant.This generalizes a result in Ref.[Wu J,Ruan Q,Yang Y H.Gradient estimates for exponentially harmonic functions on complete Riemannian manifolds.Manuscripta Mathematica,2014,143(3-4):483-489],which is covered in the case where fis a constant.