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- W1911025108 abstract "In Centro-affine invariants for smooth convex bodies [Int. Math. Res. Notices. DOI 10.1093/imrn/rnr110, 2012] Stancu introduced a family of centro-affine normal flows, $p$-flow, for $1leq p<infty .$ Here we investigate the asymptotic behavior of the planar $p$-flow for $p=infty$, in the class of smooth, origin-symmetric convex bodies. First, we prove that the $infty$-flow evolves appropriately normalized origin-symmetric solutions to the unit disk in the Hausdorff metric, modulo $SL(2).$ Second, using the $infty$-flow and a Harnack estimate for this flow, we prove a stability version of the planar Busemann-Petty centroid inequality in the Banach-Mazur distance. Third, we prove that the convergence of normalized solutions in the Hausdorff metric can be improved to convergence in the $mathcal {C}^{infty }$ topology." @default.
- W1911025108 created "2016-06-24" @default.
- W1911025108 creator A5019920891 @default.
- W1911025108 date "2015-09-09" @default.
- W1911025108 modified "2023-09-23" @default.
- W1911025108 title "The planar Busemann-Petty centroid inequality and its stability" @default.
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- W1911025108 doi "https://doi.org/10.1090/tran/6503" @default.
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