Collapsing Riemannian Metrics to Carnot-Caratheodory Metrics and Laplacians to Sub-Laplacians
Author:
- Zhong GeZGZhong Ge
- 1 June 1993
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 45 (3) , 537-553
Abstract
We study the asymptotic behavior of the Laplacian on functions when the underlying Riemannian metric is collapsed to a Carnot-Carathéodory metric. We obtain a uniform short time asymptotics for the trace of the heat kernel in the case when the limit Carnot-Carathéodory metric is almost Heisenberg, the limit of which is the result of Beal-Greiner-Stanton, and Stanton-Tartakoff.Keywords
This publication has 1 reference indexed in Scilit:
- Some regularity theorems for Carnot-Carathéodory metricsJournal of Differential Geometry, 1990