Harmonic Functions on Manifolds

Postgraduate Thesis uoadl:2878235 791 Read counter

Unit:
Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science
Deposit date:
2019-07-09
Year:
2019
Author:
Lentas Spyridon
Supervisors info:
Αντώνιος Μελάς, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
Harmonic Functions on Manifolds
Languages:
English
Translated title:
Harmonic Functions on Manifolds
Summary:
In this Master thesis we deal with harmonic functions on complete Riemannian manifolds, having
as a final goal a proof of Yau's conjecture (and eventually theorem of Colding and Minicozzi) which
states that the space of harmonic functions of polynomial growth of fixed degree d, on a
complete Riemannian manifold with non-negative Ricci curvature, M, is finite dimensional. We prove a gradient estimate for manifolds with Ricci curvature bounded from below, and derive a Liouville property and a Harnack inequality. We also prove a mean value inequality for such manifolds.
Main subject category:
Science
Keywords:
harmonic functions, manifolds, mean value inequality
Index:
No
Number of index pages:
0
Contains images:
No
Number of references:
20
Number of pages:
41
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