Analytic parametrization and volume minimization of three dimensional bodies of constant widthReportar como inadecuado




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1 LJLL - Laboratoire Jacques-Louis Lions 2 LAMA - Laboratoire de Mathématiques 3 Département de mathématiques

Abstract : We present a complete analytic parametrization of constant width bodies in dimension 3 based on the median surface: more precisely, we define a bijection between some space of functions and constant width bodies. We compute simple geometrical quantities like the volume and the surface area in terms of those functions. As a corollary we give a new algebraic proof of Blaschke-s formula. Finally, we derive weak optimality conditions for convex bodies which minimize the volume among constant width bodies.





Autor: Térence Bayen - Thomas Lachand-Robert - Edouard Oudet -

Fuente: https://hal.archives-ouvertes.fr/



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