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Heat kernel estimate on Riemannian manifolds
Date Issued
2011
Date
2011
Author(s)
Lu, Jung-Sheng
Abstract
In the common Euclidean spaces, we can explicitly express the form of heat kernel.But in the more complicated Riemannian manifolds, it is hard to express. In my survey, I will discuss in two cases, first, in complete noncompact manifold, second, in compactmanifold with convex boundary. In this two cases, we can get the same form of gradient estimate and Harnack estimate, and by these two estimates, we can get the same form ofheat kernel upper bound in these two cases. Also, by Bishop volume comparison, we can get the same form of heat kernel upper bound in these two cases. With heat kernelestimates, we can estimate the lower bound of eigenvalue of Laplace operator and Green function.
Subjects
heat kernel
Type
thesis
File(s)
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Name
ntu-100-R98221025-1.pdf
Size
23.54 KB
Format
Adobe PDF
Checksum
(MD5):53e8612e929b20cadba3d40bed456281