Papers and Preprints

• • Spectral ratios for Steklov eigenvalues of balls with revolution-type metrics. Jade Brisson, Bruno Colbois, Katie Gittins. Preprint arXiv:2403.13426 [math.SP] (20 March 2024).

  • Do the Hodge spectra distinguish orbifolds from manifolds? Part 2. Katie Gittins, Carolyn Gordon, Ingrid Membrillo Solis, Juan Pablo Rossetti, Mary Sandoval, Elizabeth Stanhope. Preprint arXiv:2311.00337 [math.DG] (1 November 2023).

  • Eigenvalue estimates for the magnetic Hodge Laplacian on differential forms. M. Egidi, K. Gittins, G. Habib, N. Peyerimhoff. J. Spectr. Theory 13 (2023), no. 4, pp. 1297–1343. DOI 10.4171/JST/480. 

  • Heat flow in polygons with reflecting edges. S. Farrington, K. Gittins. Integr. Equ. Oper. Theory 95, 27 (2023). https://doi.org/10.1007/s00020-023-02749-0. 

  • Do the Hodge spectra distinguish orbifolds from manifolds? Part 1. Katie Gittins, Carolyn Gordon, Magda Khalile, Ingrid Membrillo Solis, Mary Sandoval, Elizabeth Stanhope. Accepted 2021. Michigan Math. J. Advance Publication 1-28 (2023). DOI: 10.1307/mmj/20216126. 

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

  • Courant-sharp Robin eigenvalues for the square: the case of negative Robin parameter. K. Gittins, B. Helffer. Asymptotic Analysis, 124 (2021), 69–107, http://dx.doi.org/10.3233/ASY-201642.

  • Heat flow from polygons. M. van den Berg, P. Gilkey, K. Gittins. Potential Anal. 53 (2020), 1043-1062. https://doi.org/10.1007/s11118-019-09797-5.

  • Courant-sharp Robin eigenvalues for the square: the case with small Robin parameter. K. Gittins, B. Helffer. Ann. Math. Québec, 44 (2020), 91-123. https://doi.org/10.1007/s40316-019-00120-7.

  • Upper bounds for Courant-sharp Neumann and Robin eigenvalues. K. Gittins, C. Léna. Bull. Soc. Math. France. 148 (1), (2020), 99-132.

  • Courant-sharp Robin eigenvalues for the square and other planar domains. K. Gittins, B. Helffer. Port. Math. 76 (2019), 57-100. doi: 10.4171/PM/2027.

  • Steklov eigenvalues of submanifolds with prescribed boundary in Euclidean space. B. Colbois, A. Girouard, K. Gittins. J Geom Anal (2019) 29: 1811. https://doi.org/10.1007/s12220-018-0063-x

  • Asymptotic behaviour of cuboids optimising Laplacian eigenvalues. K. Gittins, S. Larson. Integr. Equ. Oper. Theory, 89 (2017), 607-629.

  • Minimizing Dirichlet eigenvalues on cuboids of unit measure. M. van den Berg, K. Gittins. Mathematika, 63 (2017), 469-482.

  • On the number of Courant-sharp Dirichlet eigenvalues. M. van den Berg, K. Gittins. Journal of Spectral Theory, 6 (2016), 735-745.

  • Maximising Neumann eigenvalues on rectangles. M. van den Berg, D. Bucur, K. Gittins. Bulletin of the London Mathematical Society, 48 (2016), 877-894.

  • On the heat content of a polygon. M. van den Berg, K. Gittins. J. Geom. Anal. 26 (2016), 2231–2264

  • Uniform bounds for the heat content of open sets in Euclidean space. M. van den Berg, K. Gittins. Differ. Geom. Appl. 40 (2015), 67-85.

  • Some spectral applications of McMullen's Hausdorff dimension algorithm. K. Gittins, N. Peyerimhoff, M. Stoiciu and D. Wirosoetisno. Conform. Geom. Dyn. 16 (2012), 184-203.

Survey article:

• • Courant-sharp Robin eigenvalues for the square: a review. Rendiconti Sem. Mat. Univ. Pol. Torino Vol. 77, 2 (2019), 49 – 66.