Paul Laurain's Homepage


Advances in Geometric Analysis, Paris, December 5th – 6th, 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] Classification of uniformly distributed measures of dimension 1 in general codimension, with M. Petrache, pdf

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



Last talks

Next Talk


Robin bossut, Stage M1 (printemps 2017), Théorème de la masse positive.

Nicolas Marque (2016-).