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Diastolic inequalities for the distance function min-max width of spheres
Abstract
In this article, we investigate inequalities involving the min-max width associated to the distance function and the area of two-dimensional Riemannian spheres. This geometric invariant naturally arises as min-max methods are applied for the distance function defined on the space of pairs of points. Our methods involve careful constructions of sweepouts that can be performed under the hypothesis that the Riemannian sphere does not contain stable closed geodesics. Improved bounds are obtained under further geometric assumptions (positive curvature, pinching condition, and antipodal symmetry). In the cases of a pinching condition or antipodal symmetry, our inequalities are optimal.
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BibTeX
@misc{montezuma2026diastolic,
title = {{Diastolic inequalities for the distance function min-max width of spheres}},
author = {Rafael Montezuma and Idalina Ribeiro},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05315},
eprint = {2611.05315},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05315},
}
RIS
TY - UNPB
TI - Diastolic inequalities for the distance function min-max width of spheres
AU - Rafael Montezuma
AU - Idalina Ribeiro
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05315
UR - https://arxiv.org/abs/2611.05315
AB - In this article, we investigate inequalities involving the min-max width associated to the distance function and the area of two-dimensional Riemannian spheres. This geometric invariant naturally arises as min-max methods are applied for the distance function defined on the space of pairs of points. Our methods involve careful constructions of sweepouts that can be performed under the hypothesis that the Riemannian sphere does not contain stable closed geodesics. Improved bounds are obtained under further geometric assumptions (positive curvature, pinching condition, and antipodal symmetry). In the cases of a pinching condition or antipodal symmetry, our inequalities are optimal.
ER -