Research

Calculus of Variations and quasiconformal maps

1. Regularity and compactness for critical points of degenerate polyconvex energies.
   With R. Tione. To appear in Arch. Ration. Mech. Anal.
2. Unique continuation for differential inclusions.
   With G. De Philippis and R. Tione. To appear in Ann. Inst. Henri Poincaré (C) Anal. Non Linéaire.
3. Lower semicontinuity, Stoilow factorization and principal maps.
   With K. Astala, D. Faraco, A. Koski, and J. Kristensen. Com. Pure App. Anal. 23, no. 10 (2024): 1608-1645.
4. The local Burkholder functional, quasiconvexity and Geometric Function Theory.
   With K. Astala, D. Faraco, A. Koski, and J. Kristensen. Submitted (2023).
5. Automatic quasiconvexity of homogeneous isotropic rank-one convex integrands.
   With J. Kristensen. Arch. Ration. Mech. Anal. no. 2 (2022): 479–500.
6. Numerical evidence towards a positive answer to Morrey's problem.
   With R. Teixeira da Costa. Rev. Mat. Iberoam. 38, no. 2 (2022): 601-614.
7. Remarks on Ornstein's non-inequality in R^2x2.
   With D. Faraco. Q. J. Math. 72, no. 1 (2021): 17-21.
8. Extremal rank-one convex integrands and a conjecture of Šverák.
   Calc. Var. Partial Differ. Equ. 58, no. 201 (2019).

Harmonic maps and related topics

1. Constraint maps and free boundaries.
   With A. Figalli, S. Kim and H. Shahgholian. Submitted to the Notices of the AMS (2024).
2. On the existence of degenerate solutions of the two-dimensional H-system.
   With X. Lamy and K. Zemas. Submitted (2024).
3. Constraint maps: singularities vs free boundaries.
   With A. Figalli, S. Kim, and H. Shahgholian. Submitted (2024).
4. Constraint maps with free boundaries: the Bernoulli case.
   With A. Figalli, S. Kim, and H. Shahgholian. To appear in J. Eur. Math. Soc.
5. Energy minimisers with prescribed Jacobian.
   With L. Koch and S. Lindberg. Arch. Ration. Mech. Anal. 242, no. 2 (2021): 1059-1090.
6. The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces.
   With L. Koch and S. Lindberg. Calc. Var. Partial Differ. Equ., 60, no. 55 (2021).

Stability in Analysis and Geometry

1. Optimal quantitative stability of the Möbius group of the sphere in all dimensions.
   With X. Lamy and K. Zemas. Submitted (2024).
2. Sharp quantitative stability of the Möbius group among sphere valued maps in arbitrary dimension.
   With X. Lamy and K. Zemas. To appear in Trans. Am. Math. Soc.
3. Stability of the Faber-Krahn inequality for the Short-time Fourier Transform.
   With J. Goméz, J. P. Ramos, and P. Tilli. Invent. Math. 236 (2024), 779–836.

Compensation effects in PDE

1. Compensation phenomena for concentration effects via nonlinear elliptic estimates.
   With B. Raiţă and M. Schrecker. Ars Inveniendi Analytica, Paper No. 1 (2024), 56 pp.
2. Oscillations in wave map systems and homogenization of the Einstein equations in symmetry.
   With R. Teixeira da Costa. To appear in Arch. Ration. Mech. Anal.
3. Nonlinear open mapping principles with applications to the Jacobian equation and other scale-invariant PDEs.
   With L. Koch and S. Lindberg. Adv. Math. 415 (2023): 108869.
4. Compensated Compactness: continuity in optimal weak topologies.
   With B. Raiţă and M. Schrecker. J. Funct. Anal. 283, no. 7 (2022): 109596.
5. Quasiconvexity, null Lagrangians, and Hardy integrability under constant rank constraints.
   With B. Raiţă. Arch. Ration. Mech. Anal. no. 2 (2022): 279–320.
6. On the necessity of the constant rank condition for L^p estimates.
   With B. Raiţă. C. R. Math. 358, no. 9-10 (2020): 1091-1095.