Dr Katie Gittins' Outputs (19)

Spectral ratios and gaps for Steklov eigenvalues of balls with revolution-type metrics (2024)
Journal Article
Brisson, J., Colbois, B., & Gittins, K. (in press). Spectral ratios and gaps for Steklov eigenvalues of balls with revolution-type metrics. Canadian Mathematical Bulletin,

We investigate upper bounds for the spectral ratios and gaps for the Steklov eigenvalues of balls with revolution-type metrics. We do not impose conditions on the Ricci curvature or on the convexity of the boundary. We obtain optimal upper bounds for... Read More about Spectral ratios and gaps for Steklov eigenvalues of balls with revolution-type metrics.

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
Gittins, K., Gordon, C., Khalile, M., Membrillo Solis, I., Sandoval, M., & Stanhope, E. (online). Do the Hodge spectra distinguish orbifolds from manifolds? Part 1. Michigan Mathematical Journal, 74(3), 571-598. https://doi.org/10.1307/mmj/20216126

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
Colbois, B., & Gittins, K. (2021). Upper bounds for Steklov eigenvalues of submanifolds in Euclidean space via the intersection index. Differential Geometry and its Applications, 78, Article 101777. https://doi.org/10.1016/j.difgeo.2021.101777

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
Gittins, K., & Helffer, B. (2021). Courant-sharp Robin eigenvalues for the square: The case of negative Robin parameter. Asymptotic Analysis, 124(1-2), 69-107. https://doi.org/10.3233/asy-201642

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
Gittins, K., & Léna, C. (2020). Upper bounds for Courant-sharp Neumann and Robin eigenvalues. https://doi.org/10.24033/bsmf.2800

Heat Flow from Polygons (2020)
Journal Article
van den Berg, M., Gilkey, P., & Gittins, K. (2020). Heat Flow from Polygons. Potential Analysis, 53(3), 1043-1062. https://doi.org/10.1007/s11118-019-09797-5

Courant-sharp Robin eigenvalues for the square: the case with small Robin parameter (2020)
Journal Article
Gittins, K., & Helffer, B. (2020). Courant-sharp Robin eigenvalues for the square: the case with small Robin parameter. Annales mathématiques du Québec, 44(1), 91-123. https://doi.org/10.1007/s40316-019-00120-7

Steklov Eigenvalues of Submanifolds with Prescribed Boundary in Euclidean Space (2019)
Journal Article
Colbois, B., Girouard, A., & Gittins, K. (2019). Steklov Eigenvalues of Submanifolds with Prescribed Boundary in Euclidean Space. Journal of Geometric Analysis, 29(2), 1811-1834. https://doi.org/10.1007/s12220-018-0063-x

Courant-sharp Robin eigenvalues for the square and other planar domains (2019)
Journal Article
Gittins, K., & Helffer, B. (2019). Courant-sharp Robin eigenvalues for the square and other planar domains. Portugaliae Mathematica, 76(1), 57-100. https://doi.org/10.4171/pm/2027

MINIMIZING DIRICHLET EIGENVALUES on CUBOIDS of UNIT MEASURE (2017)
Journal Article
van den Berg, M., & Gittins, K. (2017). MINIMIZING DIRICHLET EIGENVALUES on CUBOIDS of UNIT MEASURE. Mathematika, 63(2), 469-482. https://doi.org/10.1112/s0025579316000413

Asymptotic Behaviour of Cuboids Optimising Laplacian Eigenvalues (2017)
Journal Article
Gittins, K., & Larson, S. (2017). Asymptotic Behaviour of Cuboids Optimising Laplacian Eigenvalues. Integral Equations and Operator Theory, 89(4), 607-629. https://doi.org/10.1007/s00020-017-2407-5

Maximising Neumann eigenvalues on rectangles (2016)
Journal Article
van den Berg, M., Bucur, D., & Gittins, K. (2016). Maximising Neumann eigenvalues on rectangles. Bulletin of the London Mathematical Society, 48(5), 877-894. https://doi.org/10.1112/blms/bdw049

On the Heat Content of a Polygon (2016)
Journal Article
van den Berg, M., & Gittins, K. (2016). On the Heat Content of a Polygon. Journal of Geometric Analysis, 26(3), 2231-2264. https://doi.org/10.1007/s12220-015-9626-2

On the number of Courant-sharp Dirichlet eigenvalues (2016)
Journal Article
van den Berg, M., & Gittins, K. (2016). On the number of Courant-sharp Dirichlet eigenvalues. Journal of Spectral Theory, 6(4), 735-745. https://doi.org/10.4171/jst/139

Uniform bounds for the heat content of open sets in Euclidean space (2015)
Journal Article
van den Berg, M., & Gittins, K. (2015). Uniform bounds for the heat content of open sets in Euclidean space. https://doi.org/10.1016/j.difgeo.2015.01.010

Some spectral applications of McMullen's Hausdorff dimension algorithm (2012)
Journal Article
Gittins, K., Peyerimhoff, N., Stoiciu, M., & Wirosoetisno, D. (2012). Some spectral applications of McMullen's Hausdorff dimension algorithm. Conformal Geometry and Dynamics, 16, 184-203. https://doi.org/10.1090/s1088-4173-2012-00244-5

Using McMullen's Hausdorff dimension algorithm, we study numerically the dimension of the limit set of groups generated by reflections along three geodesics on the hyperbolic plane. Varying these geodesics, we found four minima in the two-dimensional... Read More about Some spectral applications of McMullen's Hausdorff dimension algorithm.