Outputs (18)

Do the Hodge spectra distinguish orbifolds from manifolds? Part 2 (2024)
Journal Article
Gittins, K., Gordon, C., Membrillo Solis, I., Pablo Rossetti, J., Sandoval, M., & Stanhope, E. (in press). Do the Hodge spectra distinguish orbifolds from manifolds? Part 2. Michigan Mathematical Journal,

Eigenvalue estimates for the magnetic Hodge Laplacian on differential forms (2023)
Journal Article
Egidi, M., Gittins, K., Habib, G., & Peyerimhoff, N. (2023). Eigenvalue estimates for the magnetic Hodge Laplacian on differential forms. Journal of Spectral Theory, 13(4), 1297-1343. https://doi.org/10.4171/JST/480

In this paper we introduce the magnetic Hodge Laplacian, which is a generalization of the magnetic Laplacian on functions to differential forms. We consider various spectral results, which are known for the magnetic Laplacian on functions or for the... Read More about Eigenvalue estimates for the magnetic Hodge Laplacian on differential forms.

Heat Flow in Polygons with Reflecting Edges (2023)
Journal Article
Farrington, S., & Gittins, K. (2023). Heat Flow in Polygons with Reflecting Edges. Integral Equations and Operator Theory, 95(4), Article 27. https://doi.org/10.1007/s00020-023-02749-0

We investigate the heat flow in an open, bounded set D in R2 with polygonal boundary ∂D. We suppose that D contains an open, bounded set D~ with polygonal boundary ∂D~. The initial condition is the indicator function of D~ and we impose a Neumann bou... Read More about Heat Flow in Polygons with Reflecting Edges.

Do the Hodge spectra distinguish orbifolds from manifolds? Part 1 (2023)
Journal Article

We examine the relationship between the singular set of a compact Riemann- ian orbifold and the spectrum of the Hodge Laplacian on p-forms by computing the heat invariants associated to the p-spectrum. We show that the heat invariants of the 0-spectr... Read More about Do the Hodge spectra distinguish orbifolds from manifolds? Part 1.

Upper bounds for Steklov eigenvalues of submanifolds in Euclidean space via the intersection index (2021)
Journal Article

We obtain upper bounds for the Steklov eigenvalues σk(M)of a smooth, compact, n-dimensional submanifold M of Euclidean space with boundary Σ that involve the intersection indices of M and of Σ. One of our main results is an explicit upper bound in te... Read More about Upper bounds for Steklov eigenvalues of submanifolds in Euclidean space via the intersection index.

Courant-sharp Robin eigenvalues for the square: The case of negative Robin parameter (2021)
Journal Article

We consider the cases where there is equality in Courant’s nodal domain theorem for the Laplacian with a Robin boundary condition on the square. In our previous two papers, we treated the cases where the Robin parameter h>0 is large, small respective... Read More about Courant-sharp Robin eigenvalues for the square: The case of negative Robin parameter.

Upper bounds for Courant-sharp Neumann and Robin eigenvalues (2020)
Journal Article

Heat Flow from Polygons (2020)
Journal Article

Courant-sharp Robin eigenvalues for the square: the case with small Robin parameter (2020)
Journal Article

Courant-sharp Robin eigenvalues for the square and other planar domains (2019)
Journal Article