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Jensen’s inequality on convex spaces. (English) Zbl 1291.53047

The author proves a Jensen inequality on \(p\)-uniformly convex spaces in terms of \(p\)-barycenters of probability measures with \((p-1)\)-th moment, with \(p\in(1,\infty)\), under a geometric condition. He also gives a Liouville-type theorem for harmonic maps described by Markov chains into a 2-uniformly convex space satisfying such a geometric condition. Finally, an alternative proof of Jensen’s inequality over Banach spaces is presented.

MSC:

53C20 Global Riemannian geometry, including pinching
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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