Neal Coleman

activity

20152022

most citedBounding Eigenvalues with Packing Density

1 citations · 1 across the 3 of their papers we have counts for

collaborators

3 papers

math.DG2022

Pólya's eigenvalue conjecture is false for spheres

Neal Coleman

By comparing the Laplace spectrum of the sphere $S^{n}$ to its Weyl function $w (x) = \frac{ω _{n}}{( 2 π ) ^{n}} ∣ S^{n} ∣ x^{n /2}$ , we show that no analogue of Pólya's eigenvalue…

math.SP2018

Laplace Subspectrality

Neal Coleman

Exploring the relationship between geometry and the resonant frequencies of a shape is of interest to pure and applied mathematicians. These resonant frequencies are related to the…

math.SP2015★ 1 cited

Bounding Eigenvalues with Packing Density

Neal Coleman

We prove a lower bound on the eigenvalues $λ_{k}$ , $k \in N$ , of the Dirichlet Laplacian of a bounded domain $Ω \subset R^{n}$ of volume $V$ : $$ λ_k \geq C_n\bigg( δ\frac…