## Differential and Integral Equations

### A compactness theorem for harmonic maps

Shoichiro Takakuwa

#### 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

https://projecteuclid.org/euclid.die/1367414141

Mathematical Reviews number (MathSciNet)
MR1608009

Zentralblatt MATH identifier
1005.58007

Subjects