Shadow Systems and Volumes of Polar Convex Bodies | Zendy

Meyer Mathieu | Zendy; Reisner Shlomo | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

Shadow Systems and Volumes of Polar Convex Bodies

Author(s) -

Meyer Mathieu,

Reisner Shlomo

Publication year - 2006

Publication title -

mathematika

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.955

H-Index - 29

eISSN - 2041-7942

pISSN - 0025-5793

DOI - 10.1112/s0025579300000061

Subject(s) - mathematics , regular polygon , reciprocal , shadow (psychology) , polytope , affine transformation , combinatorics , volume (thermodynamics) , convex body , mixed volume , function (biology) , point (geometry) , pure mathematics , convex polytope , polar , mathematical analysis , geometry , convex analysis , convex hull , convex optimization , physics , psychology , astronomy , psychotherapist , philosophy , linguistics , quantum mechanics , evolutionary biology , biology

It is proved that the reciprocal of the volume of the polar bodies, about the Santaló point, of a shadow system of convex bodies K t , is a convex function of t , thus extending to the non‐symmetric case a result of Campi and Gronchi. The case that the reciprocal of the volume is an affine function of t is also investigated and is characterized under certain conditions. These results are applied to prove an exact reverse Santaló inequality for polytopes in ℝ d that have at most d + 3 vertices.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research