The effect of curvature on convexity properties of harmonic functions and eigenfunctions

Dan Mangoubi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We give a proof of the growth bound of Laplace-Beltrami eigenfunctions due to Donnelly and Fefferman which is probably the easiest and the most elementary one. Our proof also gives new quantitative geometric estimates in terms of curvature bounds which improve and simplify previous work by Garofalo and Lin. The proof is based on a generalization of a convexity property of harmonic functions in Rn to harmonic functions on Riemannian manifolds following Agmon's ideas.

Original languageAmerican English
Pages (from-to)645-662
Number of pages18
JournalJournal of the London Mathematical Society
Volume87
Issue number3
DOIs
StatePublished - Jun 2013

Bibliographical note

Funding Information:
Received 11 January 2012; revised 17 August 2012; published online 3 December 2012. 2010 Mathematics Subject Classification 35P20, 58J50 (primary), 53C21, 35J15 (secondary). This research was supported by ISF grant 225/10 and by BSF grant 2010214.

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