Jacobian estimates and geometric inequalities under intermediate Ricci curvature
Abstract
We prove a Jacobian estimate underlying both the Heintze--Karcher comparison and the Alexandrov--Bakelman--Pucci method for submanifolds of arbitrary codimension. The estimate retains the contributions of ambient curvature along geodesics emanating from the submanifold and requires no curvature sign assumption. As applications, we obtain a quantitative Fenchel--Willmore inequality with explicit curvature remainders under nonnegative n-intermediate Ricci curvature, Michael--Simon Sobolev and isoperimetric inequalities under nonnegative (n−1)-intermediate Ricci curvature, and corresponding extensions under quadratic curvature decay. In each result, the required intermediate Ricci curvature condition depends only on the dimension of the submanifold and is independent of its codimension.
Related
- Volume Doubling and Geometric Inequalities on Graphs with Bakry-Émery Curvature
- Higher order pointwise estimates for intermediate derivative
- Synge's Theorem and a Sphere Theorem in Weighted Intermediate Ricci Curvature
- Local Topology of Riemannian Manifolds with Lower Intermediate Ricci Curvature Bounds
- Constant Rank Theorems under Intermediate Ricci Curvature
BibTeX
@misc{kwong2026jacobian,
title = {{Jacobian estimates and geometric inequalities under intermediate Ricci curvature}},
author = {Kwok-Kun Kwong and Jihye Lee and Fabio Ricci},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.13690},
eprint = {2609.13690},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13690},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Jacobian estimates and geometric inequalities under intermediate Ricci curvature
AU - Kwok-Kun Kwong
AU - Jihye Lee
AU - Fabio Ricci
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2609.13690
UR - https://arxiv.org/abs/2609.13690
AB - We prove a Jacobian estimate underlying both the Heintze--Karcher comparison and the Alexandrov--Bakelman--Pucci method for submanifolds of arbitrary codimension. The estimate retains the contributions of ambient curvature along geodesics emanating from the submanifold and requires no curvature sign assumption. As applications, we obtain a quantitative Fenchel--Willmore inequality with explicit curvature remainders under nonnegative n-intermediate Ricci curvature, Michael--Simon Sobolev and isoperimetric inequalities under nonnegative (n−1)-intermediate Ricci curvature, and corresponding extensions under quadratic curvature decay. In each result, the required intermediate Ricci curvature condition depends only on the dimension of the submanifold and is independent of its codimension.
ER -