List of all publications

  1. With F. Da Lio and J. Wettstein : Bergman-Bourgain-Brezis-type Inequality. To appear in J. of Functional Analysis [PDF ]
  2. With A. Paunoiu : Sobolev Connections and Holomorphic Structures over Kähler Surfaces. To appear in J. of Functional Analysis [PDF ]
  3. Harmonic Maps from S^3 into S^2 with low Morse Index. To appear in J. of Differential Geom. [PDF ]
  4. With A. Michelat : The Classification of Branched Willmore Spheres in the 3-Sphere and the 4-Sphere. To appear in Annales Scientifiques de l'Ecole Normale Supérieure (2021) [PDF ] Computer assisted part of the proof [PDF ]
  5. With F. Da Lio : Critical Chirality in Elliptic Systems. to appear in Annales Inst. Henri Poincaré - Analyse non linéaire (2020)[PDF ]
  6. Exploring the unknown: the work of Louis Nirenberg in Partial Differential Equations. To appear in EMS Surveys in Mathematical Sciences (2021)[PDF ]
  7. with F. Da Lio Three-commutators revisited. Comm. Partial Differential Equations 45 (2020), no. 8, 931–969. [PDF ]
  8. with F. Da Lio and F. Palmurella: A resolution of the Poisson problem for elastic plates. Arch. Ration. Mech. Anal. 236 (2020), no. 3, 1593–1676. [PDF ]
  9. Infinitely many minimal hypersufaces in low dimensions Séminaire Bourbaki, Astérisque (2020), Exp. No. 1163 [PDF ] Video : https://www.youtube.com/watch?v=afhjxjHEUl4
  10. with A. Pigati: A Proof of the Multiplicity One Conjecture for Min-Max Minimal Surfaces in Arbitrary Codimension. Duke Math. J. 169 (2020), no. 11, 2005–2044. [PDF ]
  11. with A. Pigati: The regularity of parametrized integer stationary varifolds in two dimensions. Comm. Pure Appl. Math. 73 (2020), no. 9, 1981–2042. [PDF, 608 KB]
  12. Lower Semi-Continuity of the Index in the Viscosity Method for Minimal Surfaces. Int. Math. Res. Notices 2021, no. 8, 5651-5675. [PDF, 386 KB]
  13. Willmore Minmax Surfaces and the Cost of the Sphere Eversion. J. Eur. Math. Soc. (JEMS) 23 (2021), no. 2, 349-423 [PDF, 612 KB]
  14. The Variations of Yang-Mills Lagrangian Progress in Mathematics, Springer Vol. 333, (2020) 305-379 (2020) [PDF ]
  15. with P. Laurain: Optimal estimate for the gradient of Green's function on degenerating surfaces and applications. Comm. Anal. Geom. 26 (2018), no. 4, 887-913. [PDF, 411 KB]
  16. with Y. Bernard: Uniform regularity results for critical and subcritical surface energies Calc. Var. Partial Differential Equations 58 (2019), no. 1, Art. 10, 39 pp. [PDF, 527 KB]
  17. The regularity of conformal target harmonic maps Calc. Var. Partial Differential Equations 56 (2017), no. 4. [PDF, 333 KB]
  18. with P. Laurain: Energy Quantization of Willmore surfaces at the boundary of the Moduli Space. Duke Math. J. 167 (2018), no. 11, 2073–2124. [PDF, 1016 KB]
  19. A Viscosity Method in the Min-Max Theory of Minimal Surfaces Publ. Math. Inst. Hautes Études Sci. 126 (2017), 177-246. [PDF, 544 KB]
  20. with Y. Bernard: Ends of immersed minimal and Willmore surfaces in asymtotically flat spaces Comm. Anal. Geom. 28 (2020), no. 1, 1–57. [PDF, 920 KB]
  21. Tori in $S^3$ minimizing locally the conformal volume J. Geometric Analysis 26 (2016), no. 3, 2322-2382. [PDF, 416 KB]
  22. with A. Michelat: A Viscosity Method for the Min-Max Construction of Closed Geodesics ESAIM Control Optim. Calc. Var. 22 (2016), no. 4, 1282-1324. [PDF, 544 KB]
  23. Méthodes de min-max et la conjecture de Willmore Séminaire Bourbaki, Astérisque No. 367-368 (2015), Exp. No. 1080, viii, 179-217. [PDF, 368 KB]
  24. Critical weak immersed Surfaces within Sub-manifolds of the Teichmüller Space. Advances in Math. 283 (2015), 232-274. [PDF, 320 KB]
  25. with F. Da Lio and L. Martinazzi: Blow-up analysis of a non-local Liouville-type Equation, Analysis and P.D.E. 8 (2015), no. 7, 1757-1805. [PDF, 976 KB]
  26. with P. Laurain: Optimal estimate for the gradient of Green functions on degenerating surfaces and applications Comm. Anal. Geom. 26 (2018), no. 4, 887–913. [PDF, 232 KB]
  27. with M. Petrache: The resolution of the Yang-Mills Plateau Problem in Super-critical Dimensions Advances in Math. 316 (2017), 469-540. [PDF, 560 KB]
  28. Abel Prize Lecture The work of Louis Nirenberg in Partial Differential Equations. Notices Amer. Math. Soc. 63 (2016), no. 2, 120-125. [PDF, 352 KB] Video : https://www.youtube.com/watch?v=VJWjUielWY0
  29. with A. Mondino: A frame energy for immersed tori and applications to regular homotopy classes J. Differential Geom. 104 (2016), no. 1, 143-186. [PDF, 336 KB]
  30. with R. Hardt: Sequential Weak Approximation for Maps of Finite Hessian Energy Calc. Var. Partial Differential Equations 54 (2015), no. 3, 2713-2749. [PDF, 352 KB]
  31. with M. Petrache: Global Gauges and Extensions in Optimal Spaces Analysis & P.D.E. 7 (2014), no. 8, 1851-1899. [PDF, 568 KB]
  32. with A. Mondino: Immersed Spheres of Finite Total Curvature into Manifolds. Adv. Calc. Var. 7 (2014), no. 4, 493-538. [PDF, 336 KB]
  33. with L. Keller and A. Mondino: Embedded surfaces of arbitrary genus minimizing the Willmore energy under isoperimetric constraint Arch. Ration. Mech. Anal. 212 (2014), no. 2, 645-682. [PDF, 336 KB]
  34. with P. Laurain: Angular Energy Quantization for Linear Elliptic Systems with Antisymmetric Potentials and Applications. Analysis & P.D.E. 7 (2014), no. 1, 1-41. [PDF, 448 KB]
  35. with Y. Bernard: Energy Quantization for Willmore Surfaces and Applications. Annals of Math. (2) 180 (2014), no. 1, 87-136. [PDF, 384 KB]
  36. Variational Principles for immersed Surfaces with L2-bounded Second Fundamental Form. , J. Reine Angew. Math. 695 (2014), 41-98. [PDF, 792 KB]
  37. with A. Mondino: Willmore Spheres in Compact Riemannian Manifolds. Adv. Math. 232 (2013), 608-6076. [PDF, 584 KB]
  38. Sequences of Smooth Global Isothermic Immersions. Comm. P.D.E. 38 (2013), no. 2, 276-303. [PDF, 264 KB]
  39. with P. Laurain: Energy Quantization for Biharmonic Maps. Adv. Calc. Var. 6 (2013), no. 2, 191-216. [PDF, 200 KB]
  40. with Y. Bernard: Singularity removability at branch points for Willmore surfaces. Pacific J. Math. 265 (2013), no. 2, 257-311. [PDF, 448 KB]
  41. Lipschitz conformal Immersions from degenerating Riemann Surfaces with L2-bounded Second Fundamental Forms. Adv. Calc. Var. 6 (2013), no. 1, 1-31. [PDF, 248 KB]
  42. with C. Bellettini: The regularity of Special Legendrian Integral Cycles. Ann. Sc. Norm. Sup. Pisa (5) 11 (2012), no. 1, 61-142. [PDF, 752 KB]
  43. The role of conservation laws in the analysis of conformally invariant problems. Topics in modern regularity theory, 117-167, CRM Series, 13, Ed. Norm., Pisa, 2012.
  44. with M. Petrache: Weak closure of singular abelian L^p-bundles in 3-dimensions. Geometric And Functional Analysis 21 (2011), no. 6, 1419-1442. [PDF, 616 KB]
  45. Sub-criticality of Schrödinger Systems with Antisymmetric Potentials. J. Math. Pures Appl. (9) 95 (2011), no. 3, 260-276. [PDF, 216 KB]
  46. with F. Da Lio: Sub-criticality of non-local Schrödinger systems with antisymmetric potentials and applications to half harmonic maps. Advances in Math. 227 (2011), no. 3, 1300-1348. [PDF, 744 KB]
  47. with Y. Bernard: An Energy Gap Phenomenon for Willmore Spheres, preprint 2011. [PDF, 128 KB]
  48. with F. Da Lio: 3-term commutator estimates and the regularity of 1/2-harmonic maps into spheres, Analysis and PDE 4 (2011), no. 1, 149--190. [PDF, 336 KB]
  49. with Y. Bernard: Local Palais Smale Sequences for the Willmore Functional. Comm. Analysis and Geom. 19 (2011), no. 3, 563-599. [PDF, 272 KB]
  50. with D. Pumberger: Uniqueness of tangent cones for semi-calibrated 2-cycles. Duke J. Math., 152 (2010), no 3, 441-480. [PS, 1160 KB]
  51. with M. Blaser: A Minimality property for entropic solutions to scalar conservation laws in 1 + 1 dimensions, Comm. P.D.E. 35 (2010), no. 10, 1763-1801. [PDF, 288 KB]
  52. with Gang Tian: The Singular Set of 1-1 Integral Currents, Annals of Math. (2) 169 (2009), no. 3, 741-794. [PDF, 440 KB]
  53. Analysis aspects of Willmore surfaces. Inventiones Math., 174 (2008), no.1, 1-45. [PDF, 336 KB]
  54. The role of Integrability by Compensation in Conformal Geometric Analysis. Analytic aspects of problems from Riemannian Geometry,SMF, Séminaires et Congrès, 19, (2008). [PDF, 312 KB]
  55. with T. Kessel: Singular bundles with bounded L^2 curvatures. Boll. U.M.I. volume dedicated to the memory of Guido Stampacchia, 1 (2008), no. 3, 881-901. [PDF, 208 KB]
  56. with R. Hardt: Connecting Rational Homotopy Type Singularities. Acta Math., 200 (2008), no. 1, 15-83. [PS, 1528 KB]
  57. with T. Lamm: Conservation laws for fourth order systems in four dimensions. Comm. P.D.E., 33 (2008), no. 1-3, 245-262. [PS, 632 KB]
  58. Error Analysis for the Willmore-Helfrich Functional, Oberwolfach Reports, Mathematics of Biological Membranes (2008), 2305-2309 (2008). [PDF, 88 KB]
  59. with M. Struwe: Partial regularity for harmonic maps and related problems. Comm. Pure and App. Math., 61 (2008), no. 4, 451-463. [PS, 344 KB]
  60. Conservation laws for conformally invariant variational problems. Inventiones Math., 168 (2007), no. 1, 1-22. [PS, 384 KB]
  61. Sobolev critical exponents of rational homotopy groups. Quarterly J. of Pure and App. Math., issue in honor of L.Simon, 3 (2007), no. 2, 615-630. [PS, 360 KB]
  62. Conservation laws for solutions to Schrödinger systems with antisymmetric potentials. GDR CNRS EDP Evian (2006). [PS, 328 KB]
  63. with P. Strzelecki: A sharp non-linear Gagliardo-Nirenberg-type estimate and applications to the regularity of elliptic systems. Comm. P.D.E., 30 (2005), no. 4-6, 589-604. [PS, 192 KB]
  64. Approximating J-holomorphic curves by holomorphic ones. Calc. Var. P.D.E., 21 (2004), no. 3, 273-285. [PS, 208 KB]
  65. A lower-epiperimetric inequality for area minimizing surfaces. Comm. Pure and App. Math., 57 (2004), no. 3, 273-285. [PS, 208 KB]
  66. with G. Tian: The singular set of J-holomorphic maps into algebraic varieties. Journal für Reine und Angew. Math., 570 (2004), 47-87. [PS, 528 KB]
  67. Some problems from the non-linear analysis of high dimensional Gauge Theory.Variational Analysis and applications, Volume in memory of G. Stampacchia, Erice-Sicily, (2003).
  68. with C. De Lellis: The Rectifiability of Entropy Measures in one Space dimension. Journal de Math. Pures et App., 82, (2003), no. 10, 1343-1367. [PS, 1288 KB]
  69. Bubbling, quantization and regularity issues in geometric non-linear analysis, ICM Beijing (2002). [PS, 192 KB]
  70. with L. Ambrosio, B. Kirchheim and M. Lecumberry: Rectifiability of defect measures arising in micromagnetic domains, Volume dedicated to the 80th birthday of O. Ladyzhenskaya, 29-60, Int. Math. Ser. (N.Y.), Kluwer/Plenum. [PS, 416 KB]
  71. with L. Ambrosio and M. Lecumberry: A viscosity property of minimizing micromagnetic configurations. Comm. Pure and App. Math., 56 (2003), no. 6, 681-688. [PS, 160 KB]
  72. with Y. Meyer: Partial Regularity result for a class of stationary Yang-Mills Fields. Rev. Math. Iberoamericana, 19, (2003), no.1, 195-219. [PS, 408 KB]
  73. with S. Serfaty: Compactness, kinetic formulation and entropies for a problem related to Micromagnetics. Comm. Partial Differential Equations, 28 (2003), no. 1-2, 249-269. [PS, 160 KB]
  74. with M.R. Pakzad: Weak density of smooth maps for the Dirichlet Energy between manifolds. Geom. Funct. Anal., 13 (2003), no. 1, 223-257. [PS, 336 KB]
  75. with R. Hardt: Connecting Topological Hopf Singularities. Ann. Sc. Norm. Sup. Pisa Cl. Sci. (5) 2 (2003), no. 2, 287-344. [PS, 528 KB]
  76. High-dimensional Helicities and rigidity of linked Foliations. Asian J. Math., 6, (2002), no. 3, 505-533. [PS, 536 KB]
  77. with M. Lecumberry: Regularity property for Micromagnetic configurations having zero jump energy. Calc Var. and P.D.E., 15 (2002), no. 3, 389-402. [PS, 232 KB]
  78. with F. Alouges and S. Serfaty: Wall energies of micromagnetic materials with strong planar anisotropy, ESAIM Controle Opt. Calculus Variations, a tribute to J.L. Lions (2002). [PS, 6128 KB]
  79. Parois et vortex en micromagnétisme. Journées équations aux dérivées partielles, (Forges-les-eaux, 2002), Exp. No. XIV, Univ. Nantes, Nantes 2002. [PS, 224 KB]
  80. with M. Lecumberry: The rectifiability of shock waves for the solutions of genuinely non-linear scalar conservation laws in 1+1 D, PhD Thesis of M. Lecumberry, Nantes (2002). [PS, 224 KB]
  81. Towards Jaffe and Taubes Conjectures in the strongly repulsive limit. Manuscripta Mathematica, 108 (2002), no. 2, 217-273. [PS, 568 KB]
  82. Interpolation Spaces and Energy Quantization for Yang-Mills Fields. Comm. Anal. Geom., 10 (2002), no. 4, 683-708. [PS, 216 KB]
  83. with F.H. Lin: Energy Quantization for Harmonic Maps. Duke J. Math. (2002), no. 1, 177-193. [PS, 184 KB]
  84. with F.H. Lin: Quantization property for moving Line vortices. Comm. Pure App. Math., 54, (2001), no. 7, 826-850. [PS, 376 KB]
  85. with A. Aftalion: Vortex energy and vortex bending for a rotating Bose-Einstein condensate, Physical Review A, 64, 043611 (2001), 1-7. [PS, 408 KB]
  86. with S. Serfaty: Limiting domain wall Energy for a Problem related to Micromagnetics. Comm. Pure App. Math., 54, (2001), no. 3, 294-338. [PS, 464 KB]
  87. with F.H. Lin: A Quantization property for static Ginzburg-Landau Vortices. Comm. Pure App. Math., 54, (2001), no. 2, 206-228. [PS, 352 KB]
  88. On Dense subsets of $H^{\frac{1}{2}}(S^2,S^1)$}. Glob. Anal. and Geom., 18 (2000), no. 5, 517-528.
  89. with R. Hardt: Ensembles singuliers topologiques dans les espaces fonctionnels entre variétés. Séminaire EDP, École Polytechnique, No.7, 14p, (2000-2001). [PS, 208 KB]
  90. Ginzburg Landau Vortices - The static Model. Bourbaki Seminar exposé no 868, (1999/2000), Altérisque, no. 276 (2000), 73-103.
  91. with F.H. Lin: Complex Ginzburg-Landau Equations in high dimensions and codimension 2 Minimal surfaces, J. European Math. Soc., 1, (1999) 3, 237-311.
  92. On the use of differential forms for the Skyrme Problem, Letters in Math. Phy., 45, 3, 229-238 (1998).
  93. Asymptotic analysis for the Ginzburg-Landau Equations. Mini-course ETH Zürich 1997, Bolletino UMI, 2-B, (1999) 8, no. 3, 537-575. [PDF, 288 KB]
  94. Minimizing Fibrations and $p$-Harmonic maps in Homotopy Classes from $S^3$ into $S^2$. Comm. Anal. Geom., 6, (1998), no. 3, 427-483
  95. with F. Pacard: On the set of Minimizers of the Ginzburg-Landau Functional in dimension 2. Harmonic Morphisms, Harmonic Maps and related Topics, (Brest 1997), 243-246, Pitman Research notes in Math. Series, CRC Press, 413.
  96. with D. Ye: Resolutions of the prescribed volume form equation. Non linear Diff. Equations and Applications, 3, (1996), no. 3, 323-369. [PS, 576 KB]
  97. Line vortices in the $U(1)$-Higgs Model. ESAIM Controle Optimal Calc. Var., vol 1, 1995/96, 77-167. [PDF, 644 KB]
  98. Lignes de tourbillon dans le modèle abélien de Higgs. C.R.Acad.Sc. Paris, 321, (1995), no. 1, 73-76.
  99. with F. Bethuel: Vortices for a variational problem related to Superconductivity. Annales de l'I.H.P., Analyse non linéaire, 12 (1995), no. 3, 243-303.
  100. Everywhere discontinuous Harmonic Maps into Spheres. Acta Matematica, 175, (1995), no. 2, 197-226.
  101. with F. Bethuel: Fonctionnelle de Ginzburg-Landau pour la supraconductivité, Exposé au Séminaires EDP, École Polytechnique, Exp. No. 16, 12p. (mars 1994).
  102. with D. Ye: Une résolution de l'équation à forme volume prescrite. C.R.Acad.Sc. Paris, I Math., 319, (1994), no. 1, 25-28.
  103. with H. Brezis and F. Merle: Quantization effects for $-\Delta u=u, (1-|u|^2)$ in ${\mathbb{R}}^2$}. Arch. Rat. Mech. and Anal, 126, (1994),pp 123-145.
  104. with H. Brezis and F. Merle: Effets de quantification pour $-\Delta u=u, (1-|u|^2)$ sur ${\mathbb{R}}^2$}. C.R.Acad.Sc. Paris, I Math., 317, (1993), no. 1, pp 57-60.
  105. Harmonic maps with values into Torii of revolution, published in "Applications harmoniques entre variétés": Thèse de l'université Paris 6, (1993).[PDF]
  106. Flot des applications harmoniques en dimension deux, published in "Applications harmoniques entre variétés": Thèse de l'université Paris 6, (1993).[PDF]
  107. Infinités des applications harmoniques à valeur dans une sphère pour une condition au bord donnée, published in "Applications harmoniques entre variétés": Thèse de l'université Paris 6, (1993).[PDF]
  108. Harmonic maps from $B^3$ into $S^2$ having a line of singularities, published in "Applications harmoniques entre varietes": Thèse de l'université Paris 6, (1993).[PDF]
  109. Applications harmoniques partout discontinues, Séminaires EDP, École Polytechnique, XIX, (1992).
  110. Applications harmoniques de $B^3$ dans $S^2$ partout discontinues. C.R.Acad.Sc. Paris, I Math., 314, (1992), no. 10, 719-723.
  111. Applications harmoniques de $B^3$ dans $S^2$ ayant une ligne de singularités. C.R.Acad.Sc. Paris, I Math., 313, (1991), no. 9, 583-587.
  112. with Itai Shafrir: Asymptotic analysis of minimizing harmonic maps of region bounded by two cylinders, C.R.Acad.Sc. Paris, 313, (1991), pp 503-508.