学術雑誌論文

学術雑誌論文

text

Journal of Functional Analysis. 2025, 290(1), p. 111210

A generalization of Grünbaum's inequality in RCD(0,N)-spaces

Academic Press Inc.

英語

text

2025-09-25

https://doi.org/10.1016/j.jfa.2025.111210

Brunel V.E., Ohta S.i., Serres J.. A generalization of Grünbaum's inequality in RCD(0,N)-spaces. Journal of Functional Analysis 290, 111210 (2026); https://doi.org/10.1016/j.jfa.2025.111210.

We generalize Grünbaum's classical inequality in convex geometry to curved spaces with nonnegative Ricci curvature, precisely, to (Formula presented) -spaces with N∈(1,∞) as well as weighted Riemannian manifolds of RicN≥0 for N∈(−∞,−1)∪{∞}[jls-end-space/]. Our formulation makes use of the isometric splitting theorem; given a convex set Ω and the Busemann function associated with any straight line, the volume of the intersection of Ω and any sublevel set of the Busemann function that contains a barycenter of Ω is bounded from below in terms of N. We also extend this inequality beyond uniform distributions on convex sets. Moreover, we establish some rigidity results by using the localization method, and the stability problem is also studied.

This article is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

103285

A generalization of Grünbaum's inequality in RCD(0,N)-spaces

Academic Press Inc.

英語

2025-09-25

Journal of Functional Analysis

290

1

111210

https://doi.org/10.1016/j.jfa.2025.111210

https://hdl.handle.net/11094/103285