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Generalized Variance Inequalities for Barycenters in CAT(0) and CAT(1) Spaces
We prove generalized versions of the Variance Inequality known for barycenters in CAT(0) spaces, inspired by an analogous result for $p$-uniformly convex Banach spaces. Our generalizations apply to balls of sufficiently small radius in complete CAT(1) spaces and to exponents $p \geq 2$ in the $\oper
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