Work

Petty projection inequality on the sphere and on the hyperbolic space

Year: 2025

Type: article

Abstract: We define a spherical and hyperbolic analog to the Euclidean projection body for star bodies via the gnomonic projection from the unit sphere and stereographic projection in the hyperbolid model of hyperbolic space. We then prove a spherical and hyperbolic projection inequality for these notions by using an adaption of Steiner symmetrization for spherical, respectively, hyperbolic, star bodies.

Source: Canadian Journal of Mathematics

DOI: 10.4153/s0008414x25101089

Authors: Youjiang Lin, Yuchi Wu

Institutions: University of Florence, Hebei Normal University, East China Normal University

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Natural Science Foundation of China, Science and Technology Commission of Shanghai Municipality, Hebei Normal University