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Synge's Theorem and a Sphere Theorem in Weighted Intermediate Ricci Curvature
Abstract
Using the tools developed by Kennard, Wylie, and Yeroshkin for weighted sectional curvature bounds, we generalize a theorem of Wilhelm to show that Synge's Theorem holds for manifolds with density that have positive weighted intermediate Ricci curvature and a sufficiently large first systole. Furthermore, we provide a sphere theorem for compact manifolds with positive weighted intermediate Ricci curvature.
Related
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- Hopf type theorem for surfaces of constant weighted mean curvature in Riemannian manifolds
- Constant mean curvature disks with circular boundary in the $3$-sphere and in hyperbolic space
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BibTeX
@misc{elhasan2026synges,
title = {{Synge's Theorem and a Sphere Theorem in Weighted Intermediate Ricci Curvature}},
author = {Hasan M. El-Hasan and Curtis Pro},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39015},
eprint = {2610.39015},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39015},
}
RIS
TY - UNPB
TI - Synge's Theorem and a Sphere Theorem in Weighted Intermediate Ricci Curvature
AU - Hasan M. El-Hasan
AU - Curtis Pro
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.39015
UR - https://arxiv.org/abs/2610.39015
AB - Using the tools developed by Kennard, Wylie, and Yeroshkin for weighted sectional curvature bounds, we generalize a theorem of Wilhelm to show that Synge's Theorem holds for manifolds with density that have positive weighted intermediate Ricci curvature and a sufficiently large first systole. Furthermore, we provide a sphere theorem for compact manifolds with positive weighted intermediate Ricci curvature.
ER -