f-拉普拉斯算子正调和函数的梯度估计

Gradient Estimates for Positive Harmonic Functions of f-Laplacian Operator

设M是m维完备的黎曼流形.在∞-Bakry-Emery Ricci曲率和Ricci曲率都有下界的条件下,Chen得到了f-拉普拉斯算子正调和函数的一类梯度估计.仅在∞-Bakry-Emery Ricci曲率有下界的条件下,得到了与Chen类似的梯度估计.

Let M be a m-dimensional complete Riemannian manifold.Under the assumption that both ∞-Bakry-Emery Ricci curvature and Ricci curvature are bounded from below,Chen has obtained a gradient estimate for positive harmonic functions of f-Laplacian operator.The aim of this paper is to derive the similar estimate to Chen＇s under the assumption that ∞-Bakry-Emery Ricci curvature is bounded with the lower line.