November 9, 2025Open Access

Sections and projections of the outer and inner regularizations of a convex body

Key Points

The volume of sections and projections of convex bodies was compared, emphasizing the relationships with inner and outer regularizations.
Key findings established new inequalities involving convex bodies and their geometric properties, focusing specifically on the Santaló point.
The approach is based on optimal M-estimates for isotropic convex bodies, showcasing the importance of Bizeul and Klartag's work.
These developments in geometric inequalities may enable further exploration into convex geometries and their applications in optimization.

Abstract

We establish new geometric inequalities comparing the volumes of sections and projections of a convex body, whose barycenter or Santaló point is at the origin, with those of its inner and outer regularizations. We also provide functional extensions of these inequalities to the setting of log-concave functions. Our approach relies on the recent optimal M-estimate of Bizeul and Klartag for isotropic convex bodies.

Read Full Paperexternally

Bookmark

View Full Paper

Cite This Study

Natalia Tziotziou (Tue,) studied this question.

synapsesocial.com/papers/690fdcdaf60c54d04ea38062 https://doi.org/https://doi.org/10.48550/arxiv.2511.02974