Frédéric Hélein

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

Hélein received his doctorate from the École polytechnique under Jean-Michel Coron . He was a professor at the École normal supérieure de Cachan and is a professor at the University of Paris VII (Denis Diderot). He was visiting professor at the ETH Zurich .

Hélein did pioneering work with Haïm Brézis and Fabrice Béthuel in the theory of the 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 variation problems and differential geometric problems in mathematical physics, for example in gauge theories.

Partly with his teacher Coron and with Béthuel, he also dealt with the regularity of weakly harmonic mappings between manifolds and the density of continuous mappings in Sobolew spaces of mappings between manifolds. In 1990 he showed that the weakly harmonic mappings in a sphere are regular in two dimensions (extended to higher dimensions m of the initial manifold by Lawrence C. Evans , who showed that for stationary weakly harmonic mappings the set of singular points is maximally Hausdorff dimension m -2 has). Shortly afterwards he proved a corresponding result for mappings from a two-dimensional manifold into arbitrary Riemannian manifolds, which was extended by Bethuel to higher-dimensional output manifolds (as before in the proof by LC Evans with the addition of the stationarity of the map).

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 ).

Fonts

  • with Fabrice Béthuel , Haïm Brézis : Ginzburg-Landau Vortices (= Progress in non-linear Differential Equations and their Applications. 13). Birkhäuser, Boston MA et al. 1994, ISBN 0-8176-3723-0 .
  • Applications harmoniques, lois de conservation et repères mobiles. Diderot, Paris et al. 1996, ISBN 2-84134-073-2 .
  • Constant mean curvature surfaces, harmonic maps and integrable systems. Birkhäuser, Basel et al. 2001, ISBN 3-7643-6576-5 .

Web links

Individual evidence

  1. ↑ Frédéric Hélein in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / name used
  2. ↑ Régularité des applications faiblement harmoniques entre une surface et une sphère. In: Comptes Rendus de l'Académie des Sciences de Paris. Series 1: Mathématique. Vol. 311, 1990, pp. 519-524, ( digital version (PDF; 286 kB) ).
  3. ↑ Régularité des applications faiblement harmoniques entre une surface et une variété riemanienne. In: Comptes Rendus de l'Académie des Sciences de Paris. Series 1: Mathématique. Vol. 312, 1991, pp. 591-596, ( digitized version (PDF; 288 kB) ).
personal data
SURNAME Hélein, Frédéric
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH April 22, 1963