Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Estimates of derivatives of the heat kernel
on a compact Riemannian manifold


Author: Elton P. Hsu
Journal: Proc. Amer. Math. Soc. 127 (1999), 3739-3744
MSC (1991): Primary 58G32; Secondary 60J60
DOI: https://doi.org/10.1090/S0002-9939-99-04967-9
Published electronically: May 13, 1999
MathSciNet review: 1618694
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give global estimates on the covariant derivatives of the heat kernel on a compact Riemannian manifold on a fixed finite time interval. The proof is based on analyzing the behavior of the heat kernel along Riemannian Brownian bridge.


References [Enhancements On Off] (What's this?)

  • 1. Bellanche, C., Le comportement asymptotique de $p(t,x,y)$, Asterisque, 84-85 (1981), ed. by R. Azencott.
  • 2. Hamilton, R., A matrix Harnack estimate for the heat equation, Comm. Anal. & Geom., 1 (1993), 113-126. MR 94g:58215
  • 3. Li, P. and Yau, S.-T., On the parabolic kernel of the Schrödinger operator, Acta Math., 156 (1986), 153-201. MR 87f:58156
  • 4. Malliavin, P. and Stroock, D. W., Short time behavior of the heat kernel and its logarithmic derivatives, J. of Diff. Geom., 44, No. 3 (1996), 550-570. MR 98c:58164
  • 5. Norris, J. R., Path integral formulae for heat kernels and their derivatives, Prob. Theory and Related Fields, 94 (1993), 525-541. MR 94c:58224
  • 6. Sheu, S.-J., Some estimates of the transition density function of a nondegenerate diffusion Markov process, Annals of Probability, 19, No. 2 (1991), 538-561. MR 93a:60087
  • 7. Stroock, D. W., An estimate on the Hessian of the heat kernel, Itô's Stochastic Calculus and Probability Theory, edited by N. Ikeda, S. Watanabe, M. Fukushim, and H. Kunita, Springer (1996). MR 97m:58212
  • 8. Stroock, D. W., and Turetsky, J., Upper bounds on derivatives of the logarithm of the heat kernel, preprint (1996).
  • 9. Stroock, D. W. and Zeitouni, O., Variations on a theme by Bismut, Astérisque, 236 (1996), 291-301. MR 97m:58213

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 58G32, 60J60

Retrieve articles in all journals with MSC (1991): 58G32, 60J60


Additional Information

Elton P. Hsu
Email: elton@math.nwu.edu

DOI: https://doi.org/10.1090/S0002-9939-99-04967-9
Published electronically: May 13, 1999
Additional Notes: The research was supported in part by NSF grant 9406888-DMS
Communicated by: Stanley Sawyer
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society