The effect of curvature on a convexity property of harmonic functions and eigenfunctions

Details The effect of curvature on a convexity property of harmonic functions and eigenfunctions The effect of curvature on a convexity property of harmonic functions and eigenfunctions

2011-12-19

arxiv.org/abs/1112.4352v2

Mathematics

Analysis of PDEs

19 pages. Dedication to Agmon added, abstract revised

Scientific paper

We give a proof of the Donnelly-Fefferman growth bound of Laplace-Beltrami eigenfunctions 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 an extension of a convexity property of harmonic functions in R^n to harmonic functions on Riemannian manifolds following Agmon's ideas.

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