Frédéric Hélein

Frédéric Hélein ( born April 22, 1963) is a French mathematician.

Hélein was at the École polytechnique in Jean- Michel Coron doctorate. He was a professor at the École Normale Supérieure de Cachan and is a professor at the University of Paris VII ( Denis Diderot ). He was a visiting professor at the ETH Zurich.

Hélein made ​​with Haim Brezis and Fabrice Bethuel pioneering work in the theory of Ginzburg-Landau equation, for example, they showed that the vortex for large values ​​of the parameter of the equation is determined by the values ​​of a renormalized energy. Hélein also deals with other variational problems and differential geometric problems in mathematical physics, for example, in gauge theories.

Partly with his teacher Coron and Bethuel he also dealt with the regularity of weak harmonic maps between manifolds and the density of continuous functions in Sobolev spaces of maps between manifolds. In 1990 he showed that in two dimensions the weakly harmonic maps into a sphere are ( extended to higher dimensions m of the output manifold by Lawrence C. Evans regularly, which showed that for stationary weakly harmonic maps the set of singular points maximum Hausdorff dimension m -2 ). Shortly thereafter, he proved a corresponding result for pictures of a two-dimensional manifold in arbitrary Riemannian manifolds, which has been extended to higher-dimensional output of Bethuel manifolds ( as before in the proof of LC Evans with the addition of the stationarity of the figure).

In 1999, he won the Fermat Prize with Fabrice Bethuel for contributions to the calculus of variations. In 1998 he was invited speaker at the International Congress of Mathematicians in Berlin ( Phenomena of compensation and estimates for partial differential equations ).

Writings

  • With Fabrice Bethuel, Haim Brezis: Ginzburg -Landau vortices, Birkhauser, 1994
  • Harmonic maps, conservation laws and moving frames, Cambridge Tracts in Mathematics, Cambridge University Press, 2002 ( first in 1996 in French)
  • Constant mean curvature surfaces, harmonic maps and integrable systems, Birkhäuser, 2001
Jean-Michel Coron Mathematics Genealogy Project Integrated Authority File
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