Paul Laurain's Homepage


Three days’workshop in mathematical general relativity, Lyon, April 15th – 17th, 2019.

Groupe de Travail Teichmüller


Currently, I am «Maitre de Conférence» (a kind of assitant professor position) at Univeristé Paris Diderot. Here is my complete my CV. I have done my PhD (French) under the supervision of Olivier Druet.
My PhD is about asymptotic behaviour of constant mean curvature surfaces and prescribed mean curvature problems.

I am currently Holder of the JCJC ANR BLADE .


  • Nonlinear elliptic equations with critical exponent, equations of Yamabe type, conformal invariant problems.

  • Conformal Geometry, curvature problems: minimal surfaces, CMC surfaces, Willmore surfaces, H-bubbles, Einstein metric, Yang-Mills Theory.
Paul Laurain
IMJ- Paris 7

Institut de Mathématiques de Jussieu
Equipe Géométrie et Dynamique
Bâtiment Sophie Germain
Case 7012
75205 PARIS Cedex 13
Tel:+33 01 57 27 91 00.

Bretagne, mars 2009

Publications and Preprints

[1] An obstruction to the existence of immersed curves of prescribed curvature,
with S.Kirsch, Potential Anal. 32 (2010), no. 1, 29-39. pdf

[2] Stability of the Poho\v{z}aev Obstruction in Dimension 3,
with O.Druet, J. Eur. Math. Soc. (JEMS) 12 (2010), no. 5, 1117-1149. pdf

[3] Concentration of CMC surfaces in a Riemannian manifold, 48 pages, Int. Math. Res. Not. IMRN 2012, no. 24, 5585–5649. . pdf

[4] Concentration of CMC surfaces with free boundaries,
Annales de l'Institut Henri Poincare / Analyse non lineaire,Volume 29, Issue 1, January–February 2012, Pages 109-129. pdf

[5] Angular Energy Quantization for Linear Elliptic Systems with Antisymmetric Potentials and Applications, with T.Riviere, Anal. PDE 7 (2014), no. 1, 1–41. arxiv

[6] Energy Quantization for biharmonic maps,
with T.Riviere, Advances in Calculus of Variations. Volume 6, Issue 2, Pages 191–216. pdf

[7] Stability of elliptic PDES with respect to perturbation of the domain, avec O.Druet et E.Hebey, 14 pages,
accepted dans Journal of Differential Equations . pdf

[8] Optimal estimate for the gradient of Green functions on degenerating surfaces and applications, with T.Riviere, Comm. Anal. Geom. Vol. 26, No 4, 2018., pdf

[9] Concentration of small Willmore spheres in Riemannian 3-manifolds, with A.Mondino, Anal. PDE 7 (2014), no. 8, 1901–1921., pdf

[10] Regularity and quantification for harmonic maps with free boundary, Adv. Calc. Var. 10 (2017), no. 1, 69–82., with R. Petrides pdf

[11] Energy Quantization of Willmore surfaces at the boundary of the Moduli Space, 38 pages, with T. Rivière, accepted to Dule Math. Journal, pdf

[12] A Pohozaev-type formula and Quantization of Horizontal Half-Harmonic Maps, 41 pages, with T. Da Lio and T. Rivière, pdf

[13] Analyse des Problèmes conformément invariants, 26 pages, Séminaire Laurent Schwartz, pdf

[14] Energy convexity for biharmonic maps and applications, with L. Lin, pdf

[15] Existence of Min-Max Free Boundary Disks Releasing the Width of a Manifold, with R. Petrides, accepted in Advances in Mathematics, pdf

[16] Uniqueness of Large Willmore surfaces in asymptotically flat spaces, with J. Metzger, In preparation



Last talks

Next Talk


Nicolas Marque (2016-).