PreprintCC BY-NC-ND 4.0arXiv
Sharp inequalities for the Newtonian and logarithmic capacities
Abstract
Sharp inequalities between the Riesz and logarithmic capacities of compact sets in ℝn are established, and the equality conditions are fully characterized. These results naturally extend Pólya and Szegő's conjecture on the ratio of Newtonian to logarithmic capacities in ℝ2, which was posed in the 1940s.
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BibTeX
@misc{su2026sharp,
title = {{Sharp inequalities for the Newtonian and logarithmic capacities}},
author = {Mengwei Su and Qiang Sun and Ge Xiong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04811},
eprint = {2610.04811},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04811},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Sharp inequalities for the Newtonian and logarithmic capacities
AU - Mengwei Su
AU - Qiang Sun
AU - Ge Xiong
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04811
UR - https://arxiv.org/abs/2610.04811
AB - Sharp inequalities between the Riesz and logarithmic capacities of compact sets in ℝ^n are established, and the equality conditions are fully characterized. These results naturally extend Pólya and Szegő's conjecture on the ratio of Newtonian to logarithmic capacities in ℝ^2, which was posed in the 1940s.
ER -