A conservative, regular, strongly local Dirichlet form exists on the pointed Gromov-Hausdorff limit of spaces with uniform heat kernel estimates, and the forms converge in the Mosco sense along a subsequence.
Notes on Pointed Gromov-Hausdorff Convergence
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abstract
The present article addresses to everyone who starts working with (pointed) Gromov-Hausdorff convergence. In the major part, both Gromov-Hausdorff convergence of compact and of pointed metric spaces are introduced and investigated. Moreover, the relation of sublimits occurring with pointed Gromov-Hausdorff convergence and ultralimits is discussed.
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2024 1verdicts
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Stability of heat kernel bounds under pointed Gromov--Hausdorff convergence
A conservative, regular, strongly local Dirichlet form exists on the pointed Gromov-Hausdorff limit of spaces with uniform heat kernel estimates, and the forms converge in the Mosco sense along a subsequence.