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- W4313443871 abstract "In this note we establish the weak unique continuation theorem for caloric functions on compact $RCD(K,2)$ spaces and show that there exists an $RCD(K,4)$ 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." @default.
- W4313443871 created "2023-01-06" @default.
- W4313443871 creator A5058321629 @default.
- W4313443871 creator A5072335941 @default.
- W4313443871 date "2022-12-29" @default.
- W4313443871 modified "2023-10-18" @default.
- W4313443871 title "Unique Continuation Problem on RCD Spaces. I" @default.
- W4313443871 doi "https://doi.org/10.48550/arxiv.2212.14237" @default.
- W4313443871 hasPublicationYear "2022" @default.
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