Gradient estimates of dirichlet heat semigroups and application to isoperimetric inequalities

Annals of Probability

Volumn 32, Issue 1 A, 2004, Pages 424-440

  Wang, Feng Yu ^a  

^a BEIJING NORMAL UNIVERSITY   (China)

Author keywords

Dirichlet heat semigroup; Gradient estimate; Isoperimetric inequality

Indexed keywords

EID: 2142818230     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1078415841     Document Type: Article

References (19)

1. BAKRY, D. and LEDOUX, M. (1996). Lévy-Gromov's isoperimetric inequality for an infinite-dimensional diffusion generator. Invent. Math. 123 259-281.
2. BUSER, P. (1992). A note on the isoperimetric constant. Ann. Sci. École Norm. Sup. 15 213-230.
3. CHAVEL, I. (1984). Eigenvalues in Riemannian Geometry. Academic Press, New York.
4. CHEN, M.-F. and WANG, F.-Y. (1994). Application of coupling method to the first eigenvalue on manifold. Sci. China Ser. A 37 1-14.
5. CRANSTON, M. (1991). Gradient estimates on manifolds using coupling. J. Funct. Anal. 99 110-124.
6. DONNELLY, H. and Li, P. (1982). Lower bounds for eigenvalues of Riemannian manifolds. Michigan Math. J. 29 149-161.
7. ELWORTHY, K. D. (1992). Stochastic flows on Riemannian manifolds. In Diffusion Processes and Related Problems in Analysis (M. Pinsky and V. Wihstutz, eds.) 2 37-72. Birkhäuser, Boston.
8. HU, Y.-M. (2002). A general Sobolev type inequality on Riemannian manifolds. J. Beijing Normal Univ. (Nat. Sci.) 38 445-449 (in Chinese).
9. KARATZAS, I. and SHREVE, S. E. (1998). Brownian Motion and Stochastic Calculus. Springer, Berlin.
10. KASUE, A. (1982). A Laplacian comparison theorem and function theoretic properties of a complete Riemannian manifold. Japan J. Math. 8 309-341.
11. KENDALL, W. S. (1986). Nonnegative Ricci curvature and the Brownian coupling property. Stochastic 19 111-129.
12. KENDALL, W. S. (1987). The radial part of Brownian motion on a manifold: A semimartingale property. Ann. Probab. 15 1491-1500.
13. LEDOUX, M. (1994). A simple proof of an inequality by P. Buser. Proc. Amer. Math. Soc. 121 951-958.
14. QIAN, Z. (1997). A gradient estimate on a manifold with convex boundary. Proc. Roy. Soc. Edingburgh Sect. A 127 171-179.
15. THALMAIER, A. and WANG, F.-Y. (1998). Gradient estimates for harmonic functions on regular domains in Riemannian manifolds. J. Funct. Anal. 155 109-124.
16. WANG, F.-Y. (1994). Application of coupling methods to the Neumann eigenvalue problem. Probab. Theory Related Fields 98 299-306.
17. WANG, F.-Y. (1997). On estimation of the logarithmic Sobolev constant and gradient estimates of heat semigroups. Probab. Theory Related Fields 108 87-101.
18. WANG, F.-Y. (1998). Estimates of Dirichlet heat kernels. Stochastic Process. Appl. 74 217-234.
19. WANG, F.-Y. (2000). Functional inequalities for empty essential spectrum. J. Funct. Anal. 170 219-245.