Let(M,g) be a smooth compact Riemannian manifold of dimension n.Denote△f=△-▽f.▽ the weighted Laplacian operator,where f is a smooth real valued function on M.When N is finite and the N-Bakry-Emery Ricci tensor is ...Let(M,g) be a smooth compact Riemannian manifold of dimension n.Denote△f=△-▽f.▽ the weighted Laplacian operator,where f is a smooth real valued function on M.When N is finite and the N-Bakry-Emery Ricci tensor is bounded from below by a constant,we establish local gradient estimates for positive solutions of the following simple Lichnerowicz equation△fu+cu^(-α)=0 on a compact Riemannian manifold,where α is a positive constant and c is a smooth function.展开更多
本文首先综述近年来关于微分算子W-留数的一系列研究进展。之后研究一类复合微分算子D+c(X)的基本结构,并在法坐标系下导出了微分算子的主符号表示,最终结合Lichnerowicz公式给出了5维带边流形上复合微分算子的W-留数表示。In this pape...本文首先综述近年来关于微分算子W-留数的一系列研究进展。之后研究一类复合微分算子D+c(X)的基本结构,并在法坐标系下导出了微分算子的主符号表示,最终结合Lichnerowicz公式给出了5维带边流形上复合微分算子的W-留数表示。In this paper, a series of research advances on W-residue of differential operators in recent years are reviewed. Then the basic structure of a class of complex differential operators D+c(X)is studied, and the principal symbolic representation of differential operators is derived in normal coordinate system. Finally, the W-residue representation of complex differential operators on 5-dimensional manifolds with edges is given by combining Lichnerowicz formula.展开更多
In this paper, we study Lichnerowicz type estimate for eigenvalues of drifting Laplacian operator and the decay rates of L1 and L2 energy for drifting heat equation on closed Riemannian manifolds with weighted measure.
文摘Let(M,g) be a smooth compact Riemannian manifold of dimension n.Denote△f=△-▽f.▽ the weighted Laplacian operator,where f is a smooth real valued function on M.When N is finite and the N-Bakry-Emery Ricci tensor is bounded from below by a constant,we establish local gradient estimates for positive solutions of the following simple Lichnerowicz equation△fu+cu^(-α)=0 on a compact Riemannian manifold,where α is a positive constant and c is a smooth function.
文摘本文首先综述近年来关于微分算子W-留数的一系列研究进展。之后研究一类复合微分算子D+c(X)的基本结构,并在法坐标系下导出了微分算子的主符号表示,最终结合Lichnerowicz公式给出了5维带边流形上复合微分算子的W-留数表示。In this paper, a series of research advances on W-residue of differential operators in recent years are reviewed. Then the basic structure of a class of complex differential operators D+c(X)is studied, and the principal symbolic representation of differential operators is derived in normal coordinate system. Finally, the W-residue representation of complex differential operators on 5-dimensional manifolds with edges is given by combining Lichnerowicz formula.
基金Supported by National Natural Science Foundation of China(Grant No.11271111)
文摘In this paper, we study Lichnerowicz type estimate for eigenvalues of drifting Laplacian operator and the decay rates of L1 and L2 energy for drifting heat equation on closed Riemannian manifolds with weighted measure.
