Convergence of fundamental solutions of linear parabolic equations under Cheeger-Gromov convergence

Details Convergence of fundamental solutions of linear parabolic equations under Cheeger-Gromov convergence Convergence of fundamental solutions of linear parabolic equations under Cheeger-Gromov convergence

2010-05-06

arxiv.org/abs/1005.0871v1

Mathematics

Differential Geometry

19 pages.

Scientific paper

In this note we show the convergence of the fundamental solutions of the
parabolic equations assuming the Cheeger-Gromov convergence of the underlying
manifolds and the uniform $L^1$-bound of the solutions. We also prove a local
integral estimate of fundamental solutions.

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