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Exponential Green energies, quantization, and minimizers on compact Riemann surfaces
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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BibTeX
@misc{hedenmalm2026exponential,
title = {{Exponential Green energies, quantization, and minimizers on compact Riemann surfaces}},
author = {Haakan Hedenmalm and Song-Yan Xie},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15004},
eprint = {2610.15004},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15004},
}
RIS
TY - UNPB
TI - Exponential Green energies, quantization, and minimizers on compact Riemann surfaces
AU - Haakan Hedenmalm
AU - Song-Yan Xie
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.15004
UR - https://arxiv.org/abs/2610.15004
AB - 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.
ER -