Exponential Green energies, quantization, and minimizers on compact Riemann surfaces

Haakan Hedenmalm; Song-Yan Xie

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arXiv · 2610.15004

Exponential Green energies, quantization, and minimizers on compact Riemann surfaces

Haakan Hedenmalm·Song-Yan Xie

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Abstract

We study the exponential Green energies associated with a finite point configuration on a Riemann surface. We focus on studying optimal or close-to-optimal configurations, and show that they must be well-spread out on the surface. We study in particular the round sphere and obtain values for the minimal Green energy of a configuration. The first version of this paper was written with the help of ChatGPT.

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Haakan Hedenmalm, Song-Yan Xie. 2026-10-10. Exponential Green energies, quantization, and minimizers on compact Riemann surfaces. https://arxiv.org/abs/2610.15004

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