Phanuel Mariano

collaborators

2 papers

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…

math.AP2025

Geometric properties of optimizers for the maximum gradient of the torsion function

Krzysztof Burdzy, Ilias Ftouhi, Phanuel Mariano

Consider $J (I^c ◯) := ∥\nabla u_{I^} c ◯ ∥_{\infty} / ∣ I^c ◯ ∣$ and $J_{P} (I^c ◯) := ∥\nabla u_{I^} c ◯ ∥_{\infty} / P (I^c ◯)$ , where $I^c ◯$ is a planar convex domain, $u_{I^} c ◯$ is the torsion function, $P (I^c ◯)$ …