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arXiv · 1807.09521

Plurisubharmonic geodesics and interpolating sets

Dario Cordero-Erausquin·Alexander Rashkovskii
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Abstract

We apply a notion of geodesics of plurisubharmonic functions to interpolation of compact subsets of $C^n$. Namely, two non-pluripolar, polynomially closed, compact subsets of $C^n$ are interpolated as level sets $L_t=\{z: u_t(z)=-1\}$ for the geodesic $u_t$ between their relative extremal functions with respect to any ambient bounded domain. The sets $L_t$ are described in terms of certain holomorphic hulls. In the toric case, it is shown that the relative Monge-Amp\`ere capacities of $L_t$ satisfy a dual Brunn-Minkowski inequality.

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Dario Cordero-Erausquin, Alexander Rashkovskii. 2018-07-25. Plurisubharmonic geodesics and interpolating sets. https://arxiv.org/abs/1807.09521

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