Showing math.SPShow all
2 papers · 1 filter
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.SP2025
The Second Dirichlet Eigenvalue is Simple on Every Non-equilateral Triangle, Part II: Nearly Equilateral Triangles
Ryoki Endo, Xuefeng Liu
This paper solves the open problem of the simplicity of the second Dirichlet eigenvalue for nearly equilateral triangles, offering a complete solution to Conjecture 6.47 posed by R…