Work

From intersection bodies to dual centroid bodies: A stochastic approach to isoperimetry

Year: 2024

Type: article

Abstract: We establish a family of isoperimetric inequalities for sets that interpolate between intersection bodies and dual L_{p} -centroid bodies. This provides a bridge between the Busemann intersection inequality and the Lutwak–Zhang inequality. The approach depends on new empirical versions of these inequalities.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1570

Authors: Radosław Adamczak, Grigoris Paouris, Peter Pivovarov, Paul Simanjuntak

Institutions: University of Warsaw, Princeton University, Texas A&M University, University of Missouri

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, American Institute of Mathematics

Awards: Topology and Measure in Dynamics and Operator Algebras, Convexity and stochastic isoperimetry