4 papers
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…
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…
Stable Computation of Laplacian Eigenfunctions Corresponding to Clustered Eigenvalues
Ryoki Endo, Xuefeng Liu
The accurate computation of eigenfunctions corresponding to tightly clustered Laplacian eigenvalues remains an extremely difficult problem. In this paper, using the shape differenc…
The second Dirichlet eigenvalue is simple on every non-equilateral triangle
Ryoki Endo, Xuefeng Liu
The Dirichlet eigenvalues of the Laplacian on a triangle that collapses into a line segment diverge to infinity. In this paper, to track the behavior of the eigenvalues during the…