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Results tagged with mg.metric-geometry
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user 504191
Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
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Contraction and consensus on Hadamard manifolds
I have solved this question. One can refer to Lemma 3 in the paper Decentralized Online Riemannian Optimization with Dynamic Environments. arXiv:2410.05128v1
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Contraction and consensus on Hadamard manifolds
Let $\mathcal M$ be a Hadamard manifold and $\{x_i\}_{i=1}^n\subseteq{\cal M}$ be $n$ points. Define $\{y_i\}_{i=1}^n$ as the weighted Fréchet means:
$$
y_i=\arg\min_{y\in\mathcal M}\sum_jw_{ij}d^2(y, …
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