Analytic parametrization and volume minimization of three dimensional bodies of constant widthReport as inadecuate




Analytic parametrization and volume minimization of three dimensional bodies of constant width - Download this document for free, or read online. Document in PDF available to download.

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.





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

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



DOWNLOAD PDF




Related documents