Markov type of Alexandrov spaces of nonnegative curvature

We prove that Alexandrov spaces $X$ of nonnegative curvature have Markov type 2 in the sense of Ball. As a corollary, any Lipschitz continuous map from a subset of $X$ into a 2-uniformly convex Banach space is extended as a Lipschitz continuous map on the entire space $X$.

💡 Research Summary

The paper establishes that Alexandrov spaces with non‑negative curvature possess Markov type 2, a probabilistic geometric property introduced by Ball. Markov type 2 quantifies how well a metric space preserves the expected squared distance under the transition operator of any finite‑state reversible Markov chain. Formally, a metric space (X) has Markov type 2 if there exists a constant (M) such that for every reversible Markov chain with transition matrix (P), stationary distribution (\pi), and any assignment of points ({x_i}_{i\in V}\subset X), the inequality
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