An existence theorem of harmonic functions with polynomial growth

DOI10.1090/S0002-9939-03-07060-6zbMath1046.53023OpenAlexW2119853539MaRDI QIDQ4433095

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Publication date: 29 October 2003

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-03-07060-6

zbMATH Keywords

Gromov-Hausdorff limitMoser iterationtangent cone at infinityCheng-Yau gradient estimatepersistence of Poisson's equation

Mathematics Subject Classification ID

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (11)

Local spectral convergence in \(\mathrm{RCD}^\ast(K, N)\) spaces ⋮ On the dimensions of spaces of harmonic functions with polynomial growth ⋮ Three circles theorems for harmonic functions ⋮ Rectifiability of singular sets of noncollapsed limit spaces with Ricci curvature bounded below ⋮ On the asymptotic behavior of the dimension of spaces of harmonic functions with polynomial growth ⋮ Failure of strong unique continuation for harmonic functions on RCD spaces ⋮ Harmonic functions with polynomial growth on manifolds with nonnegative Ricci curvature ⋮ The growth rate of harmonic functions ⋮ Dimension estimate of polynomial growth holomorphic functions ⋮ On the tangent cone of Kähler manifolds with Ricci curvature lower bound ⋮ Harmonic functions on asymptotic cones with Euclidean volume growth

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