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

Dan Mangoubi

doi:10.1112/jlms/jds067

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

Dan Mangoubi^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

14 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 language	English
Pages (from-to)	645-662
Number of pages	18
Journal	Journal of the London Mathematical Society
Volume	87
Issue number	3
DOIs	https://doi.org/10.1112/jlms/jds067
State	Published - 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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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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The effect of curvature on convexity properties of harmonic functions and eigenfunctions

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