[1]  Bakry D. On Sobolev and logarithmic Sobolev inequalities for Markov semigroups//Elworthy K D, Kusuoka S, Shige Kawa, eds. New Trends in Stochastic Analysis. Singapore: World Sci Publ River Edge, 1997: 43--75

[2] Bakry D, Qian Z M. Volume comparison theorems without Jacobi fields//Current Trends in Potential Theory. Bucharest: Theta, 2005: 115--122

[3] Hamiltom R S.  A matrix harnack estimate for the heat equation. Comm  Anal Geom, 1993, 1: 113--126

[4] Karp L, Li P. The heat equation on complete Riemannian manifolds. 1982, Unpublished

[5] Kotschwar B L. Hamiton's gradient estimate for the heat kernel on complete manifolds. Proc Amer Math Soc, 2007, 135(9): 3013--3019

[6] Li P, Yau S T. On the parabolic kernel of the Schr\"odinger operator. Acta Math, 1986 156: 153--201

[7] Li X D. Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds. J Math Pure Appl, 2005, 84: 1295--1361

[8] Ni L, Tam L F.  Kähler-Ricci flow and the Poincaré-Lelong equation. Comm  Anal Geom, 2004, 12(1): 111--141

[9] Qian Z M. A comparison theorem for an elliptic operator. Potential Analysis, 1998, 8: 137--142

[10] Ruan Q H. Elliptic-type gradient estimate for Schräodinger equations on noncompact manifolds. Bull Lond Math Soc, 2007, 39(6): 982--988

[11] Shi W X. Deforming the metric on complete Riemannian manifolds. J Diff Geom, 1989, 30(1): 223--301

[12] Souplet P, Zhang Q S. Sharp gradient estimate and Yau's liouville theorem theorem for the heat equation on noncompact manifolds. Bull London Math Soc, 2006, 38: 1045--1053