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An estimate for the anisotropic maximum curvature in the planar case

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Abstract

We fix a Finsler norm F and, using the anisotropic curvature flow, we prove that in the plane the anisotropic maximum curvature \(k^F_{\max }\) of a smooth Jordan curve is such that \( k^F_{\max }(\gamma )\ge \sqrt{\kappa /A}\), where A is the area enclosed by \(\gamma \) and \(\kappa \) the area of the unitary Wulff shape associated to the anisotropy F.

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  1. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli studi di Napoli Federico II, Via Cintia, Complesso Universitario Monte S. Angelo, 80126, Napoli, Italy

    Gloria Paoli

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Paoli, G. An estimate for the anisotropic maximum curvature in the planar case. Ricerche mat 71, 121–133 (2022). https://doi.org/10.1007/s11587-021-00573-5

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