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1998 A compactness theorem for harmonic maps
Shoichiro Takakuwa
Differential Integral Equations 11(1): 169-178 (1998). DOI: 10.57262/die/1367414141


We consider harmonic maps between compact Riemannian manifolds $M$, $N$ of dimension $m$, $n$ respectively. In case $m \ge 3$ we show that any set of harmonic maps with the uniformly bounded $m$-energy is compact in $C^{\infty}(M,N)$. As a corollary we obtain the gradient estimate of harmonic maps.


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Shoichiro Takakuwa. "A compactness theorem for harmonic maps." Differential Integral Equations 11 (1) 169 - 178, 1998.


Published: 1998
First available in Project Euclid: 1 May 2013

zbMATH: 1005.58007
MathSciNet: MR1608009
Digital Object Identifier: 10.57262/die/1367414141

Primary: 58E20

Rights: Copyright © 1998 Khayyam Publishing, Inc.

Vol.11 • No. 1 • 1998
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