Heat Kernels for a Class of Degenerate Elliptic Operators
Der-Chen Chang
Abstract:
In this talk, we discuss the geometry induced by a class of
second-order subelliptic operators. This class contains degenerate
elliptic and hypoelliptic operators (such as the Grushin operator and the Baouendi-Goulaouic operator). Given any two points in the
space, the number of geodesics and the lengths of those geodesics
are calculated. We find modified complex action functions and show
that the critical values of these functions will recover the
lengths of the corresponding geodesics. We also find the volume
elements by solving transport equations. Then heat kernels for
these operators are obtained. We also discuss an application of these kernels
to the Kohn Laplacian in several complex variables.