A note on the convex body isoperimetric conjecture in the plane

Author:

Wang Bo-Hshiung,Wang Ye-Kai

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 π \pi . In this note we confirm two cases of the conjecture: perturbations of the unit disk and domains bounded by curves symmetric to both coordinate axes and having exactly four vertices.

Funder

Ministry of Science and Technology, Taiwan

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference15 articles.

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3. The convex body isoperimetric conjecture in ℝ²;Berry, John;Rose-Hulman Undergrad. Math. J.,2017

4. A sharp relative isoperimetric inequality for the square;Brezis, Haim;C. R. Math. Acad. Sci. Paris,2021

5. On relative isoperimetric inequalities in the plane;Cianchi, Andrea;Boll. Un. Mat. Ital. B (7),1989

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