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

Per Ahag; Rafal Czyz

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arXiv · 2110.02604

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

Per Ahag·Rafal Czyz

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Abstract

With inspiration from the K\"ahler 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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Per Ahag, Rafal Czyz. 2021-10-06. Geodesics in the space of $m$-subharmonic functions with bounded energy. https://arxiv.org/abs/2110.02604

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