Unique continuation problem on RCD Spaces. I
Name
10711_2024_Article_890.pdf
Size
320.85 KB
Format
Adobe PDF
Checksum (MD5)
25d86164f6c1117d7150888b59c352b6
Author(s)
Deng, Qin
Zhao, Xinrui
Date Issued
February 15, 2024
Publisher
Springer Science and Business Media LLC
Citation
Geometriae Dedicata. 2024 Feb 15;218(2):42
Version
Final published version
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.
Subjects
Geometry and Topology
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10711-024-00890-7
