Abstract
Ishall discuss the connection between complex Hamiltonian mechanics and sub-Riemannian geometry on the Heisenberg group. Using these geometric concepts I shall describe the subelliptic heat kernel and its small time asymptotics. To extend this work to higher step operators I shall apply some of these concepts to a particular step 3 example.
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References
R. Beals, B. Gaveau and P. Greiner, Hamilton—Jacobi theory and the heat kernel on Heisenberg groupsJ. Math. Pures Appl. 797 (2000),633–689.
P. Greiner and O. Calin, On sub-Riemnniaan geodesics, submitted.
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© 2003 Springer Science+Business Media New York
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Greiner, P.C. (2003). Sub-Riemannian Geometry and Subelliptic PDEs. In: Kajitani, K., Vaillant, J. (eds) Partial Differential Equations and Mathematical Physics. Progress in Nonlinear Differential Equations and Their Applications, vol 52. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0011-6_9
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DOI: https://doi.org/10.1007/978-1-4612-0011-6_9
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6572-6
Online ISBN: 978-1-4612-0011-6
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