Maps from Riemannian manifolds into non-degenerate Euclidean cones
Rev. Mat. Iberoamericana, Tome 26 (2010) no. 1, p. 1057-1074 / Harvested from Project Euclid
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Let $M$ be a connected, non-compact $m$-dimensional Riemannian manifold. In this paper we consider smooth maps $\varphi: M \rightarrow \mathbb{R}^n$ with images inside a non-degenerate cone. Under quite general assumptions on $M$, we provide a lower bound for the width of the cone in terms of the energy and the tension of $\varphi$ and a metric parameter. As a side product, we recover some well known results concerning harmonic maps, minimal immersions and Kähler submanifolds. In case $\varphi$ is an isometric immersion, we also show that, if $M$ is sufficiently well-behaved and has non-positive sectional curvature, $\varphi(M)$ cannot be contained into a non-degenerate cone of $\mathbb{R}^{2m-1}$.
Publié le : 2010-09-15
Classification:  maximum principles,  harmonic maps,  isometric immersion,  Riemannian manifold,  53C42,  35B50,  53C21 
@article{1282913832,
     author = {Mari
, 
Luciano and Rigoli
, 
Marco},
     title = {Maps from Riemannian manifolds into non-degenerate Euclidean cones},
     journal = {Rev. Mat. Iberoamericana},
     volume = {26},
     number = {1},
     year = {2010},
     pages = { 1057-1074},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1282913832}
}

Mari
, 
Luciano; Rigoli
, 
Marco. Maps from Riemannian manifolds into non-degenerate Euclidean cones. Rev. Mat. Iberoamericana, Tome 26 (2010) no. 1, pp.  1057-1074. http://gdmltest.u-ga.fr/item/1282913832/