A Direct Proof of the 2nd Atiyah-Sutcliffe Conjecture for Convex Quadrilaterals

2021/12/26 by Mazen Bou Khuzam, Khuzam, Mazen Bou
Engineering · Mathematics · #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities #Structural Analysis and Optimization

paper · pdf · doi:10.48550/arxiv.2202.01061

openalex publication_date 2021/12/26 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We present a direct proof of the second conjecture made by M. Atiyah and P. Sutcliffe for the case of convex quadrilaterals. Unlike previous work on this conjecture, our proof does not require any computer aided computations. The new proof relies on a new geometric inequality proved recently by the author.

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