4 papers
Spectral partitioning of graphs into compact, connected regions
Ewan Davies, Ryan Job, Maxine Kampbell +2
We define and study a spectral recombination algorithm, SpecReCom, for partitioning a graph into a given number of connected parts. It is straightforward to introduce additional co…
Two disks maximize the third Robin eigenvalue: positive parameters
Hanna N. Kim, Richard S. Laugesen
The third eigenvalue of the Robin Laplacian on a simply-connected planar domain of given area is bounded above by the corresponding eigenvalue of a disjoint union of two equal disk…
Second Laplacian eigenvalue on real projective space
Hanna N. Kim
In this paper, we prove an upper bound on the second non-zero Laplacian eigenvalue on -dimensional real projective space. The sharp result for 2-dimensions was shown by Nadirash…
Maximization of the second Laplacian Eigenvalue on the Sphere
Hanna N. Kim
We prove a sharp isoperimetric inequality for the second nonzero eigenvalue of the Laplacian on . For , the second nonzero eigenvalue becomes maximal as the surface deg…