Work

Minimal Volume Product of Convex Bodies with Certain Discrete Symmetries and its Applications

Year: 2022

Type: article

Abstract: We give the sharp lower bound of the volume product of $n$-dimensional convex bodies that are invariant under the discrete subgroups $SO(K)=\{ g \in SO(n); g(K)=K \}$, where $K$ is an $n$-cube or $n$-simplex. This provides new partial results of Mahler’s conjecture and its nonsymmetric version. In addition, we give partial answers for Viterbo’s isoperimetric-type conjecture in symplectic geometry from the view point of Mahler’s conjecture.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnac284

Authors: Hiroshi Iriyeh, Masataka Shibata

Institutions: Ibaraki University, Meijo University

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Awards: Development of variational methods and their applications to nonlinear partial differential equations and convex geometry, Research on symplectic invariants from the viewpoint of convex geometry, Complex geometric structures and their moduli on Lie groups and homogeneous spaces, 変分的手法の発展と非線形偏微分方程式や凸幾何学への応用