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.
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A sharp inequality for torsional rigidity, perimeter, and measure is established for convex domains in R^n, extending the 2D Makai inequality with quantitative stability insights.
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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.
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The Makai inequality in higher dimensions: qualitative and quantitative aspects
A sharp inequality for torsional rigidity, perimeter, and measure is established for convex domains in R^n, extending the 2D Makai inequality with quantitative stability insights.