The Heat Kernel and Green's Function on a Manifold with Heisenberg Group as Boundary

[摘要] We study the Riemannian Laplace-Beltrami operator $L$ on a Riemannianmanifold with Heisenberg group $H_1$ as boundary. We calculate the heatkernel and Green's function for $L$, and give global and small timeestimates of the heat kernel. A class of hypersurfaces in thismanifold can be regarded as approximations of $H_1$. We also restrict$L$ to each hypersurface and calculate the corresponding heat kerneland Green's function. We will see that the heat kernel and Green'sfunction converge to the heat kernel and Green's function on theboundary.

[学科分类] 数学（综合）