Petty projection inequality on the sphere and on the hyperbolic space
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.
Authors
- Yecun Wu (ORCID: https://orcid.org/0000-0001-6011-4489)
- Lin Yang (ORCID: https://orcid.org/0000-0002-5964-3233)
Institutions
- University of Florence (IT)
- East China Normal University (CN)
- Hebei Normal University (CN)
Publication Details
- Journal
- Canadian Journal of Mathematics
- Published
- 2025-08-28
- DOI
- https://doi.org/10.4153/s0008414x25101089
- Primary Topic
- Point processes and geometric inequalities
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Natural Science Foundation of China
- Science and Technology Commission of Shanghai Municipality
- Hebei Normal University