CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

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

  Published:2004-06-01
 Printed: Jun 2004
  • Yilong Ni
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

We study the Riemannian Laplace-Beltrami operator $L$ on a Riemannian manifold with Heisenberg group $H_1$ as boundary. We calculate the heat kernel and Green's function for $L$, and give global and small time estimates of the heat kernel. A class of hypersurfaces in this manifold can be regarded as approximations of $H_1$. We also restrict $L$ to each hypersurface and calculate the corresponding heat kernel and Green's function. We will see that the heat kernel and Green's function converge to the heat kernel and Green's function on the boundary.
MSC Classifications: 35H20, 58J99, 53C17 show english descriptions Subelliptic equations
None of the above, but in this section
Sub-Riemannian geometry
35H20 - Subelliptic equations
58J99 - None of the above, but in this section
53C17 - Sub-Riemannian geometry
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/