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math.MG2024
A generalization of Grünbaum's inequality in RCD-spaces
Victor-Emmanuel Brunel, Shin-ichi Ohta, Jordan Serres
We generalize Grünbaum's classical inequality in convex geometry to curved spaces with nonnegative Ricci curvature, precisely, to -spaces with …
math.MG2022★ 1 cited
Stability estimates for the sharp spectral gap bound under a curvature-dimension condition
Max Fathi, Ivan Gentil, Jordan Serres
We study stability of the sharp spectral gap bounds for metric-measure spaces satisfying a curvature bound. Our main result, new even in the smooth setting, is a sharp quantitative…