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arXiv · 1408.4777

Every point in a Riemmanian manifold is critical

Fernando Galaz-Garcia·Luis Guijarro
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Abstract

We show that for any point $p$ in a closed Riemannian manifold $M$, there exists at least one point $q\in M$ such that $p$ is critical for the distance function from $q$. We also show that such a point $q$ cannot always be reached with geodesic loops based at $q$ with midpoint $p$.

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Fernando Galaz-Garcia, Luis Guijarro. 2014-08-20. Every point in a Riemmanian manifold is critical. https://arxiv.org/abs/1408.4777

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