Research

Geometric analysis, Spectral geometry, Nonlinear analysis on manifolds, Partial Differential Equations, Variational methods, Optimization of eigenvalues, Harmonic maps, Minimal surfaces.

(19) Regularity estimates on harmonic eigenmaps with arbitrary number of coordinates, 29 p. pdf

(18) Isoperimetric inequalities involving Steklov eigenvalues on surfaces, 28 p. pdf

(17) Extremising eigenvalues of the GJMS operators in a fixed conformal class, with Emmanuel Humbert and Bruno Premoselli, 96 p. pdf

(16) Existence of metrics maximizing the first Laplace eigenvalue on closed surfaces, with Mikhail Karpukhin and Daniel Stern, 23 p. pdf

(15) Geometric spectral optimization on surfaces, 46 p. pdf

(14) Non planar free boundary minimal disks into ellipsoids, 43 p. pdf

(13) Laplace eigenvalues and non-planar minimal spheres into 3-dimensional ellipsoids, accepted in The Journal of Geometric Analysis, 43 p. pdf

(12) A variational method for functionals depending on eigenvalues, Journal of the London Mathematical Society, Vol. 112, Issue 4, (2025) 47 p. pdf

(11) Critical metrics of eigenvalue functionals via Clarke subdifferentials, with David Tewodrose, accepted in Annales de l'institut Fourier, 62 p. pdf

(10) Shape optimization for combinations of Steklov eigenvalues on Riemannian surfaces, Mathematische Zeitschrift, 307, 13, (2024) 46 p.

(9) Asymptotics for minimizers of the Ginzburg-Landau energy with optimal regularity of the boundary data and applications, with Paul Laurain, annales de la faculté des sciences de Toulouse, Tome 33, no 5 (2024), p. 1251–1295. 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

Existence of non planar free boundary minimal disks into ellipsoids, Oberwolfach report no 36/2023, 2080--2083

I defended my Ph. D. in November, 17 2015 under the direction of Olivier Druet untitled: Eigenvalue bounds and extremal metrics.