Preprints
- B. Colbois and A. Girouard
Metric upper bounds for Steklov and Laplace eigenvalues
arXiv:2108.03101
- A. Girouard, M. Karpukhin, M. Levitin, I. Polterovich
The Dirichlet-to-Neumann map, the boundary Laplacian, and Hörmander's rediscovered manuscript
arXiv:2102.06594
Book Chapters
- 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 and accepted papers
- A. Girouard, M. Karpukhin, J. Lagacé
Continuity of eigenvalues and shape optimisation for Laplace and Steklov problems,
Geometric and Functional Analysis: Published online.
(arXiv:2004.10784)
- A. Girouard, J. Lagacé
Large Steklov eigenvalues via homogenisation on manifolds,
Inventiones mathematicae: Published online
(arXiv:2004.04044)
- A. Girouard, A. Henrot, J. Lagacé
From Steklov to Neumann via homogenisation,
Archive for Rational
Mechanics and Analysis: Volume 239 (2021), Issue 2, Pages 981-1023.
(arXiv:1906.09638)
- A. Girouard, R. Laugesen
Robin spectrum: two disks maximize the third eigenvalue.
Indiana University Mathematics Journal: Published online.
(arXiv:1907.13173)
- B. Colbois, A. Girouard, A. Hassannezhad
The Steklov and Laplacian spectra of Riemannian manifolds with boundary.
Journal of Functional Analysis: Volume 278 (2020), Issue 6.
(arXiv:1810.00711)
- B. Colbois, A. Girouard, A. Métras
Hypersurfaces with prescribed boundary and small Steklov eigenvalues
Canadian Mathematical Bulletin:
Volume 63 (2020), Issue 1.
(arXiv:1811.11463)
- B. Colbois, A. El Soufi, A. Girouard
Compact manifolds with fixed boundary and large Steklov eigenvalues.
Proceedings of the American Mathematical Society: Volume 147 (2019), Issue 9, Pages 3813–3827.
(arXiv:1701.04125)
- B. Colbois, A. Girouard, K. Gittins
Steklov eigenvalues of submanifolds with prescribed boundary in Euclidean space.
The Journal of Geometric Analysis: Volume 29 (2019), Issue 2, Pages 1811–1834.
(arXiv:1711.06458)
- A. Girouard, J. Lagacé, I. Polterovich, A. Savo
The Steklov spectrum of cuboids.
Mathematika,
Volume 65 (2019), Issue 2, Pages 272-310.
(arXiv:1711.03075)
- B. Colbois, A. Girouard, Binoy Raveendran
The Steklov spectrum and coarse discretizations of manifolds with boundary.
Pure and Applied Mathematics Quarterly: Volume 14 (2018), Issue 2, Pages 357-392.
(arXiv:1612.07665)
- D. Cianci, A. Girouard
Large spectral gaps for Steklov eigenvalues under volume constraints and under localized conformal deformations.
Annals of Global Analysis and Geometry: Volume 54 (2018), Issue 4, Pages 529–539.
(arXiv:1801.07836)
- 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)
- 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)
- 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)
- 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.
- 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)
- 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)
- A. Girouard, I. Polterovich
Upper bounds for Steklov eigenvalues on surfaces.
Electronic Research Announcements in Mathematical Sciences
,
Volume 19 (2012), Pages 77–85.
- B. Colbois, A. El Soufi, A. Girouard,
Isoperimetric control of the Steklov spectrum,
Journal of Functional
Analysis
Volume 261 (2011), Issue 5, Pages 1384-1399.
(arXiv:1103.2863)
- A. Girouard and I. Polterovich,
On the Hersch-Payne-Schiffer inequalities for Steklov
eigenvalues,
Functional Analysis and its Applications
Volume 44 (2010), Issue 2, Pages 106-117.
(arXiv:0808.2968)
- A. Girouard and I. Polterovich,
Shape optimization for low Neumann and Steklov
eigenvalues,
Mathematical Methods in the Applied Sciences
Volume 33 (2010), Issue 4, Pages 501-516.
(arXiv:0811.2617)
- A. Girouard, N. Nadirashvili, I. Polterovich,
Maximization of the second positive Neumann eigenvalue for planar domains,
Journal of Differential Geometry
Volume 83 (2009), no. 3, Pages 637-662.
(arXiv:0801.2142)
- A. Girouard,
Fundamental tone, concentration of density to points and
conformal degeneration on surfaces,
Canadian Journal of Mathematics
Volume 61 (2009), Issue 3, Pages 548-565.
(arXiv:math/0510279)
- A. Girouard,
Relative homological linking,
Topological methods in nonlinear analysis
Volume 30 (2007), Issue 2, Pages 211-222.
(arXiv:math/0311513)
Theses
- A. Girouard, Dégénérescence et problèmes
extrémaux pour les valeurs propres du laplacien sur les surfaces,
PhD, Université de Montréal, 2008.
- A. Girouard, Enlacement homologique
relatif,
MSc, Université de Montréal, 2002.
Course notes
- A. Girouard and Y. Saint-Aubin,
Mathématiques assistées par ordinateur, Université
de Montréal, 2010.
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