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On the existence of convex functions on Finsler manifolds

Published 6 Nov 2018 in math.DG | (1811.02121v2)

Abstract: We show that a non-compact (forward) complete Finsler manifold whose Holmes- Thompson volume is infinite admits no non-trivial convex functions. We apply this result to some Finsler manifolds whose Busemann function is convex.

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