Geometric analysis, Nonlinear analysis on manifolds, Partial Differential Equations, Variational methods, Optimization of eigenvalues, Harmonic maps, Minimal surfaces.
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(15) Critical metrics of eigenvalue functionals via Clarke subdifferentials, with David Tewodrose, 60 p. pdf
(14) Laplace eigenvalues and non-planar minimal spheres into 3-dimensional ellipsoids, 40 p. pdf
(13) Non planar free boundary minimal disks into ellipsoids, 42 p. pdf
(12) Maximizing one Laplace eigenvalue on n-dimensional manifolds, 42 p. pdf
(11) A variational method for functionals depending on eigenvalues, 32 p. pdf
(10) Shape optimization for combinations of Steklov eigenvalues on Riemannian surfaces, Accepted in Math. Z. 46 p.
(9) Asymptotics for minimizers of the Ginzburg-Landau energy with optimal regularity of the boundary data and applications, with Paul Laurain, accepted in Annales de la Faculté des sciences de Toulouse, 36 p. pdf
(8) Extremal metrics for combinations of Laplace eigenvalues and minimal surfaces into ellipsoids, Journal of Functional Analysis, 285 (2023), issue 10, 75 p.
(7) Existence of min-Max free boundary disks realising the width of a manifold, with Paul Laurain, Adv. Math. 352 (2019), 326–371. pdf
(6) Maximizing Steklov eigenvalues on surfaces, J. Differential Geom. 113 (2019), no. 1, 95–188.
(5) On the existence of metrics which maximize Laplace eigenvalues on surfaces, Int. Math. Res. Not. (2018), no. 14, 4261–4355.
(4) Regularity and quantification for harmonic maps with free boundary, with Paul Laurain, Adv. Calc. Var. 10 (2017), no. 1, 69–82. pdf
(3) On a rigidity result for the first conformal eigenvalue of the Laplacian, J. Spectr. Theory 5 (2015), no. 1, 227–234. pdf
(2) Existence and regularity of maximal metrics for the first Laplace eigenvalue on surfaces, Geom. Funct. Anal. 24 (2014), no. 4, 1336–1376. pdf
(1) Maximization of the second conformal eigenvalue of spheres, Proc. Amer. Math. Soc. 142 (2014), no. 7, 2385–2394. pdf
A remark on the rigidity of the first conformal Steklov eigenvalue, with Henrik Matthisen. pdf
Free boundary minimal surfaces of any topological type in Euclidean balls via shape optimization, with Henrik Matthiesen. pdf
I defended my Ph. D. in November, 17 2015 under the direction of Olivier Druet untitled: Eigenvalue bounds and extremal metrics.
Referees: Ailana Fraser, Tristan Rivière.
Jury: Nalini Anantharaman, Olivier Druet, Bernard Helffer, Paul Laurain, Tristan Rivière, Richard Schoen, Jean-Yves Welschinger.