Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Supervisors info:
Αντώνιος Μελάς, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
Harmonic Functions on Manifolds
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
