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http://arks.princeton.edu/ark:/88435/dsp01xw42nc267
Title: | Cheng-Yau Type Local Gradient Estimate for Harmonic Functions on RCD*(K,N) Metric Measure Spaces |
Authors: | Ansari, Sara |
Advisors: | Chang, Sun-Yung Alice Zhang, Ruobing |
Department: | Mathematics |
Class Year: | 2024 |
Abstract: | We present a geometric argument to prove a Cheng-Yau type local gradient estimate for positive harmonic functions on RCD*(K,N) metric measure spaces. The proof is an extension of Lihe Wang's geometric De Giorgi argument in [8] from Euclidean space to RCD*(K,N) space and uses a local uniform sobolev inequality and a local Bochner inequality established by Hua, Kell, and Xia in [6]. |
URI: | http://arks.princeton.edu/ark:/88435/dsp01xw42nc267 |
Type of Material: | Princeton University Senior Theses |
Language: | en |
Appears in Collections: | Mathematics, 1934-2024 |
Files in This Item:
File | Description | Size | Format | |
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ANSARI-SARA-THESIS.pdf | 340.64 kB | Adobe PDF | Request a copy |
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