Equipartitions and Mahler volumes of symmetric convex bodies

Autor: Matthieu Fradelizi, Alfredo Hubard, Mathieu Meyer, Edgardo Roldán-Pensado, Artem Zvavitch

Following ideas of Iriyeh and Shibata we give a short proof of the three-dimensional Mahler conjecture {\mf for symmetric convex bodies}. Our contributions include, in particular, simple self-contained proofs of their two key statements. The first of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::97e0c0bbc5609bd73e2ae8f9a21e6ba8

Dual Affine invariant points

Autor: Mathieu Meyer, Carsten Schütt, Elisabeth M. Werner

Publikováno v: Indiana University Mathematics Journal. 64:735-768

An affine invariant point on the class of convex bodies in R^n, endowed with the Hausdorff metric, is a continuous map p which is invariant under one-to-one affine transformations A on R^n, that is, p(A(K))=A(p(K)). We define here the new notion of d

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7a6e374989f9511b9730021da23c8401
https://doi.org/10.1512/iumj.2015.64.5514

Increasing functions and inverse Santaló inequality for unconditional functions.

Autor: Matthieu Fradelizi¹, Mathieu Meyer¹

Publikováno v: Positivity. Jul2008, Vol. 12 Issue 3, p407-420. 14p.

On the volume of sections of a convex body by cones

Autor: Vlad Yaskin, Matthieu Fradelizi, Mathieu Meyer

Publikováno v: Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society, American Mathematical Society, 2017, 145, pp.3153-3164. ⟨10.1090/proc/13457⟩

Let $K$ be a convex body in $\mathbb R^n$. We prove that in small codimensions, the sections of a convex body through the centroid are quite symmetric with respect to volume. As a consequence of our estimates we give a positive answer to a problem po

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fa1f2830ecbd5a7226ebfc65602f749b
http://arxiv.org/abs/1604.05351

An Application of Shadow Systems to Mahler’s Conjecture

Autor: Artem Zvavitch, Mathieu Meyer, Matthieu Fradelizi

Publikováno v: Discrete and Computational Geometry
Discrete and Computational Geometry, Springer Verlag, 2012, 48 (3), pp.721-734. ⟨10.1007/s00454-012-9435-3⟩

International audience; We elaborate on the use of shadow systems to prove a particular case of the conjectured lower bound of the volume product $\mathcal{P}(K)=\min_{z\in {\rm int}(K)}|K|||K^z|$, where $K\subset \R^n$ is a convex body and $ K^z = \

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::48266140cd91ba5997e688652b6309dc
https://doi.org/10.1007/s00454-012-9435-3