In this paper we investigate the stability of the deviation from being a sphere with respect to the isoperimetric deficit for sets of finite perimeter satisfying a mild regularity property, giving an extension to non-convex sets of the classical Bonnesen type result of Fuglede for nearly spherical domains. In particular we prove that if a set of finite perimeter E satisfies an interior cone condition with sufficiently wide angles (cf. Definition 2.1) then we have λH(E) Φ D(E) , where λH(E) is the deviation from a spherical shape with respect to the Hausdorff distance, D(E) denotes the isoperimetric deficit and Φ is an explicit function vanishing continuously at zero and depending on the dimension.

A Bonnesen type inequality involving the spherical deviation

GELLI, MARIA STELLA;
2012-01-01

Abstract

In this paper we investigate the stability of the deviation from being a sphere with respect to the isoperimetric deficit for sets of finite perimeter satisfying a mild regularity property, giving an extension to non-convex sets of the classical Bonnesen type result of Fuglede for nearly spherical domains. In particular we prove that if a set of finite perimeter E satisfies an interior cone condition with sufficiently wide angles (cf. Definition 2.1) then we have λH(E) Φ D(E) , where λH(E) is the deviation from a spherical shape with respect to the Hausdorff distance, D(E) denotes the isoperimetric deficit and Φ is an explicit function vanishing continuously at zero and depending on the dimension.
2012
Gelli, MARIA STELLA; Fusco, N; Pisante, G.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/155493
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