On a generalization of the Blaschke-Lebesgue theorem for disk-polygons

TL;DR

This paper extends the Blaschke-Lebesgue theorem to disk-polygons, broadening its applicability, and offers a new proof of the original theorem, enhancing understanding of convex domain optimization.

Contribution

It generalizes the Blaschke-Lebesgue theorem to disk-polygons and presents a novel proof, expanding theoretical insights into convex geometry.

Findings

Extension of the theorem to disk-polygons

New proof of the classical Blaschke-Lebesgue theorem

Broader understanding of convex domain properties

Abstract

In this paper we prove an extension of the Blaschke-Lebesgue theorem for a family of convex domains called disk-polygons. Also, this provides yet another new proof of the Blaschke-Lebesgue theorem.