# Harmonic maps from Riemannian polyhedra to geodesic spaces with curvature bounded from above

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No abstract available.

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Retractions are a prevalent tool in Riemannian optimization that provides a way to smoothly select a curve on a manifold with given initial position and velocity. We review and propose several retractions on the manifold $${\mathcal {M}}_r$$ of rank- $$r$$ $$m\times n$$ matrices. With the...

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Given an arbitrary pseudo-Riemanniaa maaifold (M,g), consider a real function f, defined on M, whose Hessian with respect to the initial pseudo-Riemannian metric g is non-degenerate. Then we obtain a new pseudo-Riemannian manifold (M,h), where h = âˆ‡g2f. The aim of this work is twofold....

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Let $$(M,g)$$ be a (complete) Riemannian surface, and let $$\Omega \subset M$$ be an open subset whose closure is homeomorphic to a disk. We prove that if $$\partial \Omega $$ is smooth and it satisfies a strong concavity assumption, then there are at least two distinct orthogonal geodesics in...