An estimate on the Hessian of the heat kernel

Daniel W. Stroock
Additional contact information
Daniel W. Stroock: Massachusetts Institute of Technology, Department of Mathematics

A chapter in Itô’s Stochastic Calculus and Probability Theory, 1996, pp 355-371 from Springer

Abstract: Summary Let M be a compact, connected Riemannian manifold, and let p t (x, y) denote the fundamental solution to Cauchy initial value problem for the heat equation $$\frac{\partial u}{\partial t}=\frac{1}{2}\Delta u$$ , where Δ is the Levi-Civita Laplacian. The purpose of this note is to show that the Hessian of log p t (·, y) at x is bounded above by a constant times $$\frac{1}{t}+\frac{dist{{\left( x,y \right)}^{2}}}{{{t}^{2}}}$$ for t ∈ (0, 1].

Keywords: Heat Kernel; Ricci Flow; Heat Kernel Estimate; Brownian Path; Connected Riemannian Manifold (search for similar items in EconPapers)
Date: 1996
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-4-431-68532-6_23

Ordering information: This item can be ordered from
http://www.springer.com/9784431685326

DOI: 10.1007/978-4-431-68532-6_23

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().