Asymptotic formulas for heat kernels
and Green's functions.
Courant Institute, (UC Irvine next year)
Wednesday, March 14
2:45-3:45 pm, Room 4419
We study the behavior of heat kernels and Green's functions of the
Laplacian operator on complete Riemannian manifolds (with a lower
bound in Ricci curvature) that converge, in the measured
Gromov-Hausdorff sense, to a limit space. By studying the analysis
on these limit spaces, in particular, tangent cones at infinity, we
get a unified treatment of the asymptotic formulas for heat kernels
and Green's functions. This gives natural new proofs of the asymptotic
formulas of Li, Colding-Minicozzi and Li-Tam-Wang.