General Lp affine isoperimetric inequalities
Christoph Haberl, Franz E. Schuster
TL;DR
This paper establishes sharp Lp affine isoperimetric inequalities for Lp projection and centroid bodies, strengthening existing inequalities and advancing the understanding of geometric properties in convex analysis.
Contribution
The paper introduces new sharp inequalities for Lp projection and centroid bodies, extending and strengthening classical affine isoperimetric inequalities.
Findings
Sharp Lp affine isoperimetric inequalities for Lp projection bodies
Sharp Lp affine isoperimetric inequalities for Lp centroid bodies
Strengthening of Lp Petty projection and Lp Busemann--Petty centroid inequalities
Abstract
Sharp Lp affine isoperimetric inequalities are established for the entire class of Lp projection bodies and the entire class of Lp centroid bodies. These new inequalities strengthen the Lp Petty projection and the Lp Busemann--Petty centroid inequality.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsPoint processes and geometric inequalities · Mathematical Inequalities and Applications · Mathematics and Applications