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math.SP2026
Monotonicity of the first Dirichlet eigenvalue of regular polygons
Joel Dahne, Javier Gómez-Serrano, Joana Pech-Alberich
In this paper we prove that the first Dirichlet eigenvalue of an -sided regular polygon of fixed area is a monotonically decreasing function of for all , a…
math.SP2021
A counterexample to Payne's nodal line conjecture with few holes
Joel Dahne, Javier Gómez-Serrano, Kimberly Hou
Payne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must touch the boundary of the domain. In their 1997 breakthrough paper, Hoffmann-Ostenhof, Hoff…