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math.AP2026
Maximizing the fundamental Laplace--Neumann eigenvalue on quadrilaterals
Ryoki Endo, Braxton Osting
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 N…
math.SP2026
Sharp Dirichlet eigenvalue inequalities on triangles
Ryoki Endo, Xuefeng Liu, Phanuel Mariano
We prove sharp Dirichlet eigenvalue inequalities for planar triangles. We settle a conjecture of Laugesen and Siudeja by showing that the equilateral triangle uniquely minimizes a…