English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Following ideas of Iriyeh and Shibata we give a short proof of thethree-dimensional Mahler conjecture {\mf for symmetric convex bodies}. Ourcontributions include, in particular, simple self-contained proofs of their twokey statements. The first of these is an equipartition (ham sandwich type)theorem which refines a celebrated result of Hadwiger and, as usual, can beproved using ideas from equivariant topology. The second is an inequalityrelating the product volume to areas of certain sections and their duals. Weobserve that these ideas give a large family of convex sets in every dimensionfor which the Mahler conjecture holds true. Finally we give an alternativeproof of the characterization of convex bodies that achieve the equality caseand establish a {\mf new} stability result.

Equipartitions and Mahler volumes of symmetric convex bodies