Sub-Riemannian Geometry and Subelliptic PDEs

  • Peter C. Greiner
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 52)


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.


Heat Kernel Heisenberg Group Hamiltonian Flow Subelliptic Operator Heisenberg Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. Beals, B. Gaveau and P. Greiner, Hamilton—Jacobi theory and the heat kernel on Heisenberg groupsJ. Math. Pures Appl. 797 (2000),633–689.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    P. Greiner and O. Calin, On sub-Riemnniaan geodesics, submitted.Google Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Peter C. Greiner
    • 1
  1. 1.Mathematics Department University of TorontoTorontoCanada

Personalised recommendations