Paul Laurain's Homepage

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Minicours about Gemeral Relativity (Jan Metzger)

Workshop on Free boundary in conformal geometry(Coming soon)

Situation

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. Here are the slides of my defence (French).

Interests

  • 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
France
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, accepted for publication in I.M.R.N. . 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, 38 pages. 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, 18 pages, pdf

[9] Concentration of small Willmore spheres in Riemannian 3-manifolds, with A.Mondino, 19 pages, Accepted to Analysis&PDE, pdf

[10] Regularity and quantification for harmonic maps with free boundary, Accepted in Advances in Calculus of Variations, 16 pages, with R. Petrides pdf

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

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

Communications

Last talks

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Student:

Nicolas Marque (2016-).

Teaching