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- W4301201991 abstract "Let $M$ be a connected, non-compact $m$-dimensional Riemannian manifold. In this paper we consider smooth maps $phi: M to mathbb{R}^n$ 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 $phi$ and a metric parameter. As a side product, we recover some well known results concerning harmonic maps, minimal immersions and Kahler submanifolds. In case $phi$ is an isometric immersion, we also show that, if $M$ is sufficiently well-behaved and has non-positive sectional curvature, $phi(M)$ cannot be contained into a non-degenerate cone of $mathbb{R}^{2m-1}$." @default.
- W4301201991 created "2022-10-05" @default.
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- W4301201991 date "2010-03-30" @default.
- W4301201991 modified "2023-10-16" @default.
- W4301201991 title "Maps from Riemannian manifolds into non-degenerate Euclidean cones" @default.
- W4301201991 doi "https://doi.org/10.48550/arxiv.1003.5772" @default.
- W4301201991 hasPublicationYear "2010" @default.
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