Fundamental solutions for a family of sub-elliptic PDEs (Q938576)

The authors survey the behavior of geodesics relative to a family of subelliptic operators and especially to the sub-Laplacian on Heisenberg group. The complex action function and the volume element along geodesics are discussed. Using the above two tools, the authors obtain the fundamental solution and the heat kernel for the sub-Laplacian. A brief discussion on application to magnetic resonance imaging is also given.