Research interests
Research interests
I am interested in nonlinear variational problems arising in conformal geometry. My main expertise lies in equations and systems at the critical scale, where conformal invariance gives rise to both geometric structures and analytical difficulties. More specifically, I have studied questions of regularity, compactness, and the variational construction of solutions for n-harmonic maps and their p-harmonic approximations, free-boundary and fractional problems, Willmore surfaces, and conformally invariant curvature energies in higher dimensions.
With Katarzyna Mazowiecka and Armin Schikorra: On minimizing W^{s,1/s}-maps between circles, arXiv:2606.15713, 2026.
With Katarzyna Mazowiecka and Armin Schikorra: Minimizing and non-minimizing degree-one W^{s,1/s}-harmonic maps between spheres, arXiv:2606.15644, 2026.
With Katarzyna Mazowiecka and Rémy Rodiac: Min-max n-harmonic maps of degree 1 with free boundary into S^{n-1} in almost round balls, arXiv:2605.28668, 2026
With Yann Bernard, Tian Lan and Tristan Rivière: The Regularity of Critical Points to Scale-Invariant Curvature Energies in Dimension 4, arXiv:2511.01765, hal-05416182, 2025.
With Tristan Rivière: Weak immersions with second fundamental form in a critical Sobolev space, arXiv:2510.10594, hal-05416167, 2025.
With Nicolas Marque: Some global properties of umbilic points of Willmore immersions in the 3-sphere, arXiv:2506.10720, hal-05117589, 2025.
With Katarzyna Mazowiecka and Rémy Rodiac: A weak energy identity for (n+α)-harmonic maps with a free boundary in a sphere, arXiv:2503.21523, hal-05009466, 2025.
A duality theorem for a four dimensional Willmore energy, arXiv:2308.11433, hal-04838402, 2023.
With Katarzyna Mazowiecka and Armin Schikorra: Existence of nontrivial n-harmonic maps via min-max methods, arXiv:2601.05700, Calculus of Variations and Partial Differential Equations, 2026.
With Paul Laurain: Huber Theorem revisited in dimensions 2 and 4, arXiv:2502.05541, hal-05004709, The Journal of Geometric Analysis, 2025.
With Tristan Rivière: Construction of harmonic coordinates for weak immersions, arXiv:2510.10601, hal-05416150, International Mathematics Research Notices, 2025.
Classification of branched Willmore spheres in codimension 1, arXiv:2306.07965, hal-04838400, Proceedings of the American Mathematical Society, 2023.
Regularity of unconstrained p-harmonic maps from curved domain and application to critical p-Laplace systems, arXiv:2407.13236, hal-04838405, Potential Analysis, 2024.
Energy quantization for Willmore surfaces with bounded index, arXiv:2305.08668, hal-04838382, Journal of the European Mathematical Society, 2023.
With Armin Schikorra: A note on limiting Calderon-Zygmund theory for transformed n-Laplace systems in divergence form, arXiv:2404.01922, hal-04838367, Bulletin of the London Mathematical Society, 2024.
With Armin Schikorra: Regularizing properties of n-Laplace systems with antisymmetric potentials in Lorentz spaces, arXiv:2305.05961, hal-04838377, Mathematische Annalen, 2023.
With Tian Lan and Tristan Rivière: The Analysis of Willmore Surfaces and its Generalizations in Higher Dimensions, arXiv:2511.01777, hal-05416174, Journal of Mathematical Study, 2025. Special issue in the honor of Gang Tian.