Displaying similar documents to “Comparing the relative volume with the relative inradius and the relative width.”

A quantitative version of the isoperimetric inequality : the anisotropic case

Luca Esposito, Nicola Fusco, Cristina Trombetti (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We state and prove a stability result for the anisotropic version of the isoperimetric inequality. Namely if E is a set with small anisotropic isoperimetric deficit, then E is “close” to the Wulff shape set.

Characterization of convex functions

Jacek Tabor, Józef Tabor (2009)

Studia Mathematica

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There are many inequalities which in the class of continuous functions are equivalent to convexity (for example the Jensen inequality and the Hermite-Hadamard inequalities). We show that this is not a coincidence: every nontrivial linear inequality which is valid for all convex functions is valid only for convex functions.