Nilima Nigam

most citedHow large can the first eigenvalue be on a surface of genus two?

11 citations · 11 across the 3 of their papers we have counts for

collaborators

3 papers

math.NA2025

At the intersection of Numerical Analysis and Spectral Geometry

Nilima Nigam

How do the geometric properties of a domain impact the spectrum of an operator defined on it? How do we compute accurate and reliable approximations of these spectra? The former qu…

math.NA2025

The spectrum of the Steklov-Helmholtz operator

Nilima Nigam, Kshitij Patil, Weiran Sun

We present a wavenumber-robust strategy for computing Steklov eigenpairs of the Helmholtz operator $- Δ - μ^{2}$ . As the wavenumber $μ \to μ_{D}$ from below (where $μ_{D}^{2}$ is a Di…

math.SP2005★ 11 cited

How large can the first eigenvalue be on a surface of genus two?

D. Jakobson, M. Levitin, N. Nadirashvili +2

Sharp upper bounds for the first eigenvalue of the Laplacian on a surface of a fixed area are known only in genera zero and one. We investigate the genus two case and conjecture th…