Journal of the Mathematical Society of Japan

Harmonic functions on asymptotic cones with Euclidean volume growth

Shouhei HONDA

Full-text: Open access

Abstract

We study harmonic functions with polynomial growth on asymptotic cones of a nonnegatively Ricci curved manifold with Euclidean volume growth. Especially, we will give the classification of such harmonic functions.

Article information

Source
J. Math. Soc. Japan, Volume 67, Number 1 (2015), 69-126.

Dates
First available in Project Euclid: 22 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1421936546

Digital Object Identifier
doi:10.2969/jmsj/06710069

Mathematical Reviews number (MathSciNet)
MR3304015

Zentralblatt MATH identifier
1317.53051

Subjects
Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 53C43: Differential geometric aspects of harmonic maps [See also 58E20]

Keywords
Gromov-Hausdorff convergence Ricci curvature Lipschitz functions and harmonic functions

Citation

HONDA, Shouhei. Harmonic functions on asymptotic cones with Euclidean volume growth. J. Math. Soc. Japan 67 (2015), no. 1, 69--126. doi:10.2969/jmsj/06710069. https://projecteuclid.org/euclid.jmsj/1421936546


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