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Quantitative Rigidity of Ricci Nonnegative Manifolds via the Regular Green Constant
Abstract
For a Ricci non-negative non-parabolic manifold (Mn≥3,g), assuming the minimal normalized Green function admits the asymptotic expansion G=r2−n+Hp+O1(r), we prove the scaling invariant defect HpRn−2 controls the geometry of the geodesic ball quantitatively, 1/RdGH(Bp(R),B0ℝn(R))≤ Cn (Hp Rn−2)1/(88(n+1)(4n+1)).
Related
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BibTeX
@misc{huang2026quantitative,
title = {{Quantitative Rigidity of Ricci Nonnegative Manifolds via the Regular Green Constant}},
author = {Zhelei Huang and Bijia Luo and Jie Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36998},
eprint = {2610.36998},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36998},
}
RIS
TY - UNPB
TI - Quantitative Rigidity of Ricci Nonnegative Manifolds via the Regular Green Constant
AU - Zhelei Huang
AU - Bijia Luo
AU - Jie Zhou
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36998
UR - https://arxiv.org/abs/2610.36998
AB - For a Ricci non-negative non-parabolic manifold (M^n≥3,g), assuming the minimal normalized Green function admits the asymptotic expansion G=r^2−n+H_p+O_1(r), we prove the scaling invariant defect H_pR^n−2 controls the geometry of the geodesic ball quantitatively, 1/Rd_GH(B_p(R),B_0^ℝ^n(R))≤ C_n (H_p R^n−2)^1/(88(n+1)(4n+1)).
ER -