Hamilton–Jacobi theory and the heat kernel on Heisenberg groups

The subelliptic geometry of Heisenberg groups is worked out in detail and related to complex Hamiltonian mechanics. The two geometric pictures are essential for complete understanding of the heat equation for the subelliptic Laplacian. We give a complete description of the geodesics and obtain preci...

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Bibliographic Details
Published in:Journal de mathématiques pures et appliquées 2000-09, Vol.79 (7), p.633-689
Main Authors: Beals, Richard, Gaveau, Bernard, Greiner, Peter C
Format: Article
Language:English
Subjects:
Carnot–Caratheodory metric
Differential geometry
Exact sciences and technology
Geometry
Global analysis, analysis on manifolds
Group theory
Hamiltonian mechanics
Heisenberg group
Mathematical analysis
Mathematics
Partial differential equations
Sciences and techniques of general use
Sub-Riemannian geometry
Subelliptic diffusion
Topological groups, lie groups
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:The subelliptic geometry of Heisenberg groups is worked out in detail and related to complex Hamiltonian mechanics. The two geometric pictures are essential for complete understanding of the heat equation for the subelliptic Laplacian. We give a complete description of the geodesics and obtain precise global estimates and small-time asymptotics of the heat kernel.
ISSN:0021-7824
DOI:10.1016/S0021-7824(00)00169-0