A note on the convex body isoperimetric conjecture in the plane

Bo-Hshiung Wang; Ye-Kai Wang

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arXiv · 2104.04954

A note on the convex body isoperimetric conjecture in the plane

Bo-Hshiung Wang·Ye-Kai Wang

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Abstract

The convex body isoperimetric conjecture in the plane asserts that the least perimeter to enclose given area inside a unit disk is greater than inside any other convex set of area $\pi$. In this note we confirm two cases of the conjecture: domains symmetric to both coordinate axes and perturbations of unit disk.

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Bo-Hshiung Wang, Ye-Kai Wang. 2021-04-11. A note on the convex body isoperimetric conjecture in the plane. https://arxiv.org/abs/2104.04954

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