On the volume product of planar polar convex bodies — Lower estimates with stability

DOI10.1556/SScMath.50.2013.2.1235zbMath1313.52007arXiv1507.01481OpenAlexW2963444591MaRDI QIDQ2937512

Shlomo Reisner, Endre jun. Makai, Károly jun. Böröczky, Mathieu Meyer

Publication date: 9 January 2015

Published in: Studia Scientiarum Mathematicarum Hungarica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.01481

zbMATH Keywords

stabilitylower estimatesBanach-Mazur distanceBlaschke-Santaló inequalitySantaló pointMahler conjecturereverse Blaschke-Santaló inequalityvolume product in the plane

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Convex sets in (2) dimensions (including convex curves) (52A10)

Related Items (8)

Minimal volume product of three dimensional convex bodies with various discrete symmetries ⋮ Symmetric Mahler's conjecture for the volume product in the \(3\)-dimensional case ⋮ On densities of lattice arrangements intersecting every \(i\)-dimensional affine subspace ⋮ Optimization of the anisotropic Cheeger constant with respect to the anisotropy ⋮ Stability of the reverse Blaschke-Santaló inequality for unconditional convex bodies ⋮ Flag numbers and floating bodies ⋮ Polytopes of maximal volume product ⋮ Numerical shape optimization among convex sets

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