Three circles theorems for harmonic functions

DOI10.1007/s00208-016-1366-5zbMath1357.58028arXiv1601.02066OpenAlexW3104589972MaRDI QIDQ343174

Guoyi Xu

Publication date: 25 November 2016

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.02066

zbMATH Keywords

polynomial growthharmonic functionstangent conesconic measure of powermaximal volume growthmetric conesnon-negative Ricci curvaturenon-negative sectional curvatureThree Circles Theoremsuniform bound

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Elliptic equations on manifolds, general theory (58J05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Harmonic maps, etc. (58E20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items (12)

On the dimensions of spaces of harmonic functions with polynomial growth ⋮ On the asymptotic behavior of the dimension of spaces of harmonic functions with polynomial growth ⋮ On the three-circle theorem and its applications in Sasakian manifolds ⋮ Failure of strong unique continuation for harmonic functions on RCD spaces ⋮ Three balls theorem for eigenfunctions of Dirac operator in Clifford analysis ⋮ Harmonic and Schrödinger functions of polynomial growth on gradient shrinking Ricci solitons ⋮ Matrix Li-Yau-Hamilton estimates under Ricci flow and parabolic frequency ⋮ Harmonic functions with polynomial growth on manifolds with nonnegative Ricci curvature ⋮ The growth rate of harmonic functions ⋮ Dimension estimate of polynomial growth holomorphic functions ⋮ Three circle theorems for eigenfunctions on complete shrinking gradient Ricci solitons with constant scalar curvature ⋮ A CR Analogue of Yau’s Conjecture on Pseudoharmonic Functions of Polynomial Growth

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