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Collapsing Riemannian Metrics to Carnot-Caratheodory Metrics and Laplacians to Sub-Laplacians

Published online by Cambridge University Press:  20 November 2018

Zhong Ge
Zhong Ge*
Affiliation:
Department of Mathematics, University of Arizona, Tucson, Arizona 85721, U.S.A.
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Abstract

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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

58G2535H05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 3 , 01 June 1993 , pp. 537 - 553
Copyright
Copyright © Canadian Mathematical Society 1993

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