Dan Mangoubi
Published 2011-12-19, updated 2012-07-25Version 3
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 a convexity property of harmonic functions on curved manifolds, generalizing Agmon's Theorem on a convexity property of harmonic functions in R^n.
Comments: 24 pages. This is a major revision. The main theorem now treats the case of pinched curvature between any two real values. The proof is simplified in several points. Ricci curvature is replaced by sectional curvature. Referee's remarks incorporated
Journal: J. Lond. Math. Soc. 87 (2013), no. 3, 645--662
A few sharp estimates of harmonic functions with applications to Steklov eigenfunctions
Isoperimetric inequalities and regularity of $A$-harmonic functions on surfaces
Isoperimetric inequalities and geometry of level curves of harmonic functions on smooth and singular surfaces
![QR code for arXiv:1112.4352 [math.AP]](http://oss.arxitics.com/images/favicon.svg)