On the uniqueness for the heat equation on complete Riemannian manifolds

Fei He; Man Chun Lee

doi:10.1007/s10455-020-09738-1

On the uniqueness for the heat equation on complete Riemannian manifolds

Fei He, Man Chun Lee^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We prove some uniqueness result for solutions to the heat equation on Riemannian manifolds. In particular, we prove the uniqueness of L^p solutions with 0 < p< 1 and improves the L¹ uniqueness result of Li (J Differ Geom 20:447–457, 1984) by weakening the curvature assumption.

Original language	English (US)
Pages (from-to)	497-504
Number of pages	8
Journal	Annals of Global Analysis and Geometry
Volume	58
Issue number	4
DOIs	https://doi.org/10.1007/s10455-020-09738-1
State	Published - Nov 1 2020

Funding

The first named author would like to thank Prof. Jiaping Wang for helpful communication. The first named author was partially supported by the National Natural Science Foundation of China (No. 11801474), Fundamental Research Funds for the Central Universities (No. 20720180007) and Natural Science Foundation of Fujian Province (No. 2019J05011). The second named author was partially supported by NSF Grant DMS-1709894.

Keywords

Complete noncompact manifolds
Heat equation on manifolds
Uniqueness problem

ASJC Scopus subject areas

Analysis
Political Science and International Relations
Geometry and Topology

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10.1007/s10455-020-09738-1

Cite this

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On the uniqueness for the heat equation on complete Riemannian manifolds

Abstract

Funding

Keywords

ASJC Scopus subject areas

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