✦ LIBER ✦

Heat Equation Derivative Formulas for Vector Bundles

✍ Scribed by Bruce K. Driver; Anton Thalmaier

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 411 KB
Volume: 183
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2001.3746

No coin nor oath required. For personal study only.

✦ Synopsis

We use martingale methods to give Bismut type derivative formulas for differentials and co-differentials of heat semigroups on forms, and more generally for sections of vector bundles. The formulas are mainly in terms of Weitzenbo ck curvature terms; in most cases derivatives of the curvature are not involved. In particular, our results improve B. K. Driver's formula in (1997, J. Math. Pures Appl. (9) 76, 703 737) for logarithmic derivatives of the heat kernel measure on a Riemannian manifold. Our formulas also include the formulas of K. D.

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