Sub-Riemannian Geometry and Subelliptic PDEs
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.
KeywordsHeat Kernel Heisenberg Group Hamiltonian Flow Subelliptic Operator Heisenberg Manifold
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