Unique continuation problem on RCD Spaces. I
Author(s)
Deng, Qin; Zhao, Xinrui
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In this note we establish the weak unique continuation theorem for caloric functions on compact <jats:italic>RCD</jats:italic>(<jats:italic>K</jats:italic>, 2) spaces and show that there exists an <jats:italic>RCD</jats:italic>(<jats:italic>K</jats:italic>, 4) space on which there exist non-trivial eigenfunctions of the Laplacian and non-stationary solutions of the heat equation which vanish up to infinite order at one point . We also establish frequency estimates for eigenfunctions and caloric functions on the metric horn. In particular, this gives a strong unique continuation type result on the metric horn for harmonic functions with a high rate of decay at the horn tip, where it is known that the standard strong unique continuation property fails.
Date issued
2024-02-15Department
Massachusetts Institute of Technology. Department of MathematicsPublisher
Springer Science and Business Media LLC
Citation
Geometriae Dedicata. 2024 Feb 15;218(2):42
Version: Final published version
ISSN
0046-5755
1572-9168
Keywords
Geometry and Topology