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.
|Autori:||Gelli M; Fusco N; Pisante G|
|Titolo:||A Bonnesen type inequality involving the spherical deviation|
|Anno del prodotto:||2012|
|Digital Object Identifier (DOI):||10.1016/j.matpur.2012.05.006|
|Appare nelle tipologie:||1.1 Articolo in rivista|