On Harnack estimates for positive solutions of the heat equation on a complete manifold;Inégalités de Harnack pour les solutions positives de l'équation de la chaleur sur une variété complète

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 324, Issue 9, 1997, Pages 1037-1042

  Bakry, Dominique ^a   Qian, Zhongmin ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031138826     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0764-4442(97)87882-2     Document Type: Article

References (10)

1. [1] Bakry D. and Emery M., 1985. Diffusions hypercontractives, Sém. Probab. XIX, Lecture Notes in Math. 1123, Springer-Verlag, pp. 177-206.
2. [2] Bakry D. and Qian Z., 1996. Gradient estimates and Harnack inequality on a complete manifold, preprint.
3. [3] Bakry D. and Qian Z., 1996. Harnack inequalities on a manifold with positive or negative Ricci curvature, preprint.
4. [4] Cheeger J. and Yau S.-T., 1981. A lower bound for the heat kernel, Comm. Pure Appl. Math., 34, pp. 465-480.
5. [5] Davies E. B., 1989. Heat Kernels and Spectral Theory, Cambridge Tracts in Math., Cambridge Univ. Press, 92.
6. [6] Li P. and Yau S.-T., 1986. On the parabolic kernel of the Schrödinger operator, Acta Math., 156, pp. 153-201.
7. [7] Sturm K.-T., 1992. Heat kernel bounds on manifolds, Math. Ann., 292, p. 149-162.
8. [8] Yau S.-T., 1975. Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math., 28, pp. 201-228.
9. [9] Yau S.-T., 1994. On the Harnack inequalities of partial differential equations, Comm. Anal. Geom., 2(3), pp. 431-450.
10. [10] Yau S.-T., 1995. Harnack inequality for non-self-adjoint evolution equations, Math. Res. Lett., 2, pp. 387-399.