Asymptotic of the Green's Function of a Riemannian Manifold and Ito's Stochastic Integrals

1 February 1974

journal article
Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences

Vol. 71 (2) , 381-383
https://doi.org/10.1073/pnas.71.2.381

Abstract

Quantitative estimates are obtained by comparison with ordinary differential equations associated to a subharmonic exhaustion function q. We associate with q a ratio a, which can be considered as the heat flow in an intrinsic time, and the sup and the inf of a, namely a(+) and a(-), on the level hypersurfaces of q. Then a(+) and a(-) define heat flows on the real line. Comparison between the heat flow on the manifold and heat flows on the line are obtained by stochastic integrals.

Keywords

FUNCTION
DIFFERENTIAL
MANIFOLD
STOCHASTIC
ORDINARY
SUP
ITO'S
EXHAUSTION
ASYMPTOTIC
SUBHARMONIC

This publication has 1 reference indexed in Scilit:

ON POSITIVE GREEN'S FUNCTIONS
Proceedings of the National Academy of Sciences, 1954