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

Ge, Zhong

Canadian journal of mathematics, Tome 45 (1993) no. 3, pp. 537-553

Résumé

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.

Détail

DOI : 10.4153/CJM-1993-028-6

Mots-clés : 58G25, 35H05

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