Publications

Preprints
  1. B. Colbois, A. El Soufi, A. Girouard
    Compact manifolds with fixed boundary and large Steklov eigenvalues.
    (arXiv:1701.04125)

  2. B. Colbois, A. Girouard, Binoy Raveendran
    The Steklov spectrum and coarse discretizations of manifolds with boundary.
    (arXiv:1612.07665)

Book Chapters
  1. A. Girouard and I. Polterovich
    Spectral geometry of the Steklov problem. Shape optimization and spectral theory,
    120-148. De Gruyter Open Ltd, Warsaw/Berlin. 2017.
Published Papers
  1. A. Girouard and I. Polterovich
    Spectral geometry of the Steklov problem.
    Journal of spectral theory, Volume 7 (2017), Issue 2, Pages 321–359.
    (arXiv:1411.6567)

  2. A. Girouard, R. Laugesen, B. Siudeja
    Steklov eigenvalues and quasiconformal maps of simply connected planar domains.
    Archive for Rational Mechanics and Analysis
    Volume 219 (2016), Issue 2, Pages 903-936.
    (arXiv:1412.8073)

  3. A. Girouard, L. Parnovski, I. Polterovich, D. Sher
    The Steklov spectrum of surfaces: asymptotics and invariants.
    Mathematical Proceedings of the Cambridge Philosophical Society.
    Volume 157 (2014), Issue 3, Pages 379-389.)
    (arXiv:1311.5533)

  4. B. Colbois and A. Girouard,
    The spectral gap of graphs and Steklov eigenvalues on surfaces.
    Electronic Research Announcements in Mathematical Sciences ,
    Volume 21 (2014), Pages 19–27.

  5. B. Colbois, A. Girouard, M. Iversen,
    Uniform stability of the Dirichlet spectrum for rough outer perturbations,
    Journal of Spectral Theory
    Volume 3 (2013), Issue 4, Pages 575–599.
    (arXiv:1206.2616)

  6. B. Colbois, A. El Soufi, A. Girouard,
    Isoperimetric control of the spectrum of a compact hypersurface,
    Journal für die reine und angewandte Mathematik
    Issue 683 (2013), Pages 49-65.
    (arXiv:1007.0826)

  7. A. Girouard, I. Polterovich
    Upper bounds for Steklov eigenvalues on surfaces.
    Electronic Research Announcements in Mathematical Sciences ,
    Volume 19 (2012), Pages 77–85.

  8. B. Colbois, A. El Soufi, A. Girouard,
    Isoperimetric control of the Steklov spectrum,
    Journal of Functional Analysis
    Vol 261 (2011), Issue 5, Pages 1384-1399.
    (arXiv:1103.2863)

  9. A. Girouard and I. Polterovich,
    On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues,
    Functional Analysis and its Applications
    Vol 44 (2010), no. 2, Pages 106-117.
    (arXiv:0808.2968)

  10. A. Girouard and I. Polterovich,
    Shape optimization for low Neumann and Steklov eigenvalues,
    Mathematical Methods in the Applied Sciences
    Vol 33 (2010), Issue 4, Pages 501-516.
    (arXiv:0811.2617)

  11. A. Girouard, N. Nadirashvili, I. Polterovich,
    Maximization of the second positive Neumann eigenvalue for planar domains,
    Journal of Differential Geometry
    Vol 83 (2009), no. 3, Pages 637-662.
    (arXiv:0801.2142)

  12. A. Girouard,
    Fundamental tone, concentration of density to points and conformal degeneration on surfaces,
    Canadian Journal of Mathematics
    Vol 61 (2009), no. 3, Pages 548-565.
    (arXiv:math/0510279)

  13. A. Girouard,
    Relative homological linking,
    Topological methods in nonlinear analysis
    Vol 30 (2007), no. 2, Pages 211-222.
    (arXiv:math/0311513)

Theses

  1. A. Girouard, Dégénérescence et problèmes extrémaux pour les valeurs propres du laplacien sur les surfaces,
    PhD, Université de Montréal, 2008.

  2. A. Girouard, Enlacement homologique relatif,
    MSc, Université de Montréal, 2002.


Course notes

  1. A. Girouard and Y. Saint-Aubin, Mathématiques assistées par ordinateur, Université de Montréal, 2001.