Thierry Aubin

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Thierry Aubin 1976

Thierry Émilien Flavien Aubin (born May 6, 1942 in Béziers ; † March 21, 2009 ) was a French mathematician who dealt with differential geometry and nonlinear partial differential equations .

Life

Aubin studied from 1961 at the École polytechnique and received his doctorate in 1969 under André Lichnerowicz . From 1968 to 1973 he was a professor at the University of Lille and then at the University of Paris VI Pierre et Marie Curie .

Act

In 1976, Aubin showed that Kähler manifolds (compact complex manifolds with Kähler metric) with negative first Chern class allow unambiguously determined Kähler-Einstein metrics, which Eugenio Calabi had suspected. In a certain way, this theorem generalizes the uniformization theorem of Henri Poincaré for Riemann surfaces (Poincaré showed in 1896 that these are surfaces of negative curvature for genus greater than 1) to higher dimensions. He worked on the theorem for almost twelve years since his dissertation and carried out the proof of this theorem of global differential geometry with local methods he developed using nonlinear partial differential equations of the Monge-Ampere type . Shing-Tung Yau then dealt shortly thereafter with the case of the disappearing Chern class and thus solved the Calabi conjecture, for which he received the Fields Medal.

His work on the problem of Hidehiko Yamabe was also important , who in 1960 believed he had found a proof that the metric of a Riemannian manifold can be brought into the form of a metric with constant scalar curvature by conformal transformations. Yamabe's “proof” turned out to be flawed ( Neil Trudinger ) because he applied variation methods to a nonlinear partial differential equation of the elliptic type that occurred in the proof, but which failed in this “non-compact” problem. Aubin analyzed the failure of Yamabe's proof and recognized the importance of the focal points of the minimizing functions of the problem of variation. His analysis became important in the theory of nonlinear partial differential equations ( Haïm Brézis , Louis Nirenberg , Pierre-Louis Lions ). The Yamabe problem was finally solved by Richard Schoen in 1984.

Aubin has been a corresponding member since 1990 and a full member since 2003 of the Académie des Sciences , whose Prix Servant he received in 1982.

Fonts

  • Nonlinear Analysis on Manifolds. Monge-Ampere Equations , Springer, Basic Teachings of Mathematical Sciences 1982, ISBN 0387907041 .
  • A Course in Differential Geometry , American Mathematical Society 2001, ISBN 082182709X .
  • Some Nonlinear Problems in Riemannian Geometry , Springer-Verlag 1998, ISBN 3540607528 .

literature

  • En hommage à Thierry Aubin , SMF Gazette des Mathématiciens 121, July 2009, pp. 71–85 (French and English; obituaries; with two images)

Web links

References

  1. ↑ Aubin Equations du type Monge-Ampère sur les variétés kählériennes compactes , Comptes Rendus, Vol. 283, 1976, pp. 116-120, Bulletin Sci. Math., Vol. 102, 1978, pp. 63-95
  2. ^ Aubin Equations différentielles non-linéaires et probème de Yamabe concernant la courbure scalaire , J. Math. Pures Appl., Vol. 55, 1976, pp. 269-296
personal data
SURNAME Aubin, Thierry
ALTERNATIVE NAMES Aubin, Thierry Émilien Flavien (full name)
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH May 6, 1942
PLACE OF BIRTH Beziers
DATE OF DEATH March 21, 2009