The equilateral triangle uniquely minimizes the scale-invariant functional of the first Dirichlet eigenvalue, area, and perimeter, settling the Laugesen-Siudeja conjecture and yielding an optimal two-term lower bound.
At the intersection of numerical analysis and spectral geometry
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Sharp Dirichlet eigenvalue inequalities on triangles
The equilateral triangle uniquely minimizes the scale-invariant functional of the first Dirichlet eigenvalue, area, and perimeter, settling the Laugesen-Siudeja conjecture and yielding an optimal two-term lower bound.