Author

B. Osting

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Preprint Sep 2026

Maximizing the fundamental Laplace--Neumann eigenvalue on quadrilaterals

We prove that among convex planar quadrilaterals of equal area, the square uniquely maximizes the first nonzero Laplace--Neumann eigenvalue. This is the quadrilateral case of the Neumann analogue of the long-standing P\'olya--Szeg\H{o} conjecture, which asserts that the regular $n$-gon minimizes the first Laplace--Diri...

Ryoki Endo, Braxton Osting · 1 citation