November 8, 2025

The Isoperimetric-Type Inequality For Projection Entropy

Key Points

Stronger inequalities for projection entropy are introduced, enhancing classical understanding of convex bodies.
Key evidence shows connections to isoperimetric and Urysohn inequalities, expanding mathematical frameworks.
Approach includes employing p-quermassintegrals to establish new theoretical results concerning geometry and entropy.
Significance may enhance further explorations in geometric measure theory and its applications in various fields.

Abstract

The projection entropy of convex bodies in ℝ n is introduced. By using introduced p-quermassintegrals, we prove an isoperimetric-type inequality for projection entropy. Some stronger inequalities than the classical isoperimetric inequality and the dual Urysohn inequality are obtained.

Bookmark

Cite This Study

Yin et al. (Fri,) studied this question.

synapsesocial.com/papers/690e8b6ca5b062d7a4e7356a https://doi.org/https://doi.org/10.1142/s0129167x26500126