Differential and Integral Equations

A compactness theorem for harmonic maps

Shoichiro Takakuwa

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Abstract

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.

Article information

Source
Differential Integral Equations, Volume 11, Number 1 (1998), 169-178.

Dates
First available in Project Euclid: 1 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367414141

Mathematical Reviews number (MathSciNet)
MR1608009

Zentralblatt MATH identifier
1005.58007

Subjects
Primary: 58E20: Harmonic maps [See also 53C43], etc.

Citation

Takakuwa, Shoichiro. A compactness theorem for harmonic maps. Differential Integral Equations 11 (1998), no. 1, 169--178. https://projecteuclid.org/euclid.die/1367414141


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