Geodesics in the space of $m$-subharmonic functions with bounded energy

Abstract

With inspiration from the Kähler geometry, we introduce a metric structure on the energy class, ${\mathcal{E}}_{1,m}$, of $m$-subharmonic functions with bounded energy and show that it is complete. After studying how the metric convergence relates to the accepted convergences in this Caffarelli-Nirenberg-Spruck model, we end by constructing geodesics in a subspace of our complete metric space.

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