Grassmannian forms of LXYZ's L p $L^p$ upper L Superscript p affine Sobolev inequality chain
Abstract
Abstract In this article, we reformulate LXYZ’s L p $L^p$ upper L Superscript p affine Sobolev inequality chain (including Lutwak–Yang–Zhang’s L p $L^p$ upper L Superscript p affine Sobolev inequality and Xiao’s p -affine capacity inequality) in the setting of Grassmann manifolds. For this purpose, the Grassmannian p $ p $ p -affine capacity is introduced.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Geometric Analysis and Curvature Flows
Contact Mechanics and Variational Inequalities
Publication details
- Journal / source
- Canadian Mathematical Bulletin
- Publisher
- Canadian Mathematical Society
- Volume
- 69
- Issue
- 3
- Pages
- 927–943
- Publication date
- 2 January 2026
- Language
- EN