List of publications

Research area

Analysis of Partial Differential Equations - PDE - arising in physics and geometry, calculus of variations, geometric analysis, application of geometric measure theory to PDE, the geometry of structures of singularities, shock and defects for weak solutions to elliptic, parabolic and hyperbolic PDE's.

Research seminar: Analysis seminar

Selected publications

Everywhere discontinuous Harmonic Maps into Spheres, Acta Matematica, 175, (1995), 197-226
Bubbling, quantization and regularity issues in geometric non-linear analysis, ICM Beijing (2002) [PS, 192 KB]
with Fang-Hua Lin: Energy Quantization for Harmonic Maps. Duke Math. J. (2002), no. 1, 177-193. [PS, 184 KB]
Conservation laws for conformally invariant variational problems. Inventiones Math., 168 (2007), 1-22 [PS, 384 KB]
with Robert Hardt: Connecting rational homotopy type singularities of maps between manifolds. Acta Matematica, 200 (2008), 15-83 [PS, 1528 KB]
Analysis Aspects of Willmore Surfaces. Inventiones Math., 174 (2008), no. 1, 1-45 [PDF, 336 KB]
with Gang Tian: The singular set of 1-1 Integral currents. Annals of Math., 169 (2009), no. 3, 741-794 [PDF, 440 KB]
with David Pumberger: Uniqueness of tangent cones for semi-calibrated 2-cycles. Duke Math. J. 152 (2010), no 3, 441-480. [PS, 1160 KB]
by Sylvia Serfaty Conservation laws and compensated regularity for antisymmetric systems and Willmore surfaces (after Tristan Rivière) Séminaire Bourbaki. Vol. 2009/2010. Exposés 1012–1026. Astérisque No 339 (2011)
with Yann Bernard: Energy Quantization for Willmore Surfaces and Applications. Annals of Math., (2) 180 (2014), no. 1, 87-136 [PDF, 384 KB]
A viscosity method in the min-max theory of minimal surfaces. Publications mathématiques de l'IHÉS, 126 (2017), no. 1, 177-246 [PDF, 544 KB]
with Paul 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]
with Alessandro 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, 1016 KB]
Willmore Minmax Surfaces and the Cost of the Sphere Eversion. J. Eur. Math. Soc. (JEMS) 23 (2021), no. 2, 349-423 [PDF, 612 KB]
with Riccardo Caniato: The Unique Tangent Cone Property for Weakly Holomorphic Maps into Projective Algebraic Varieties Duke Math. J. to appear in 2022.

Books and monographs

with Frank Pacard: Linear and Non-linear Aspects of Vortices. Birkhäuser (2000)
Conformally Invariant Variational Problems (2012) [PDF, 1048 KB]
Weak Immersions of Surfaces with $L^2$-bounded second fundamental form. PCMI Graduate Summer School (2013) [PDF, 600 KB]
The Variations of Yang-Mills Lagrangian. 9th Differential Geometry Summer School. KIAS (2014) [PDF, 592 KB]
Minmax Methods in the Calculus of Variations of Curves and Surfaces (2016) [www]