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.
Citation
Shoichiro Takakuwa. "A compactness theorem for harmonic maps." Differential Integral Equations 11 (1) 169 - 178, 1998. https://doi.org/10.57262/die/1367414141
Information
