Thierry Aubin

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

Life

Aubin studied from 1961 at the École Polytechnique and received his PhD in 1969 with André Lichnerowicz. 1968 to 1973 he was professor at the University of Lille and then at the University of Paris VI Pierre et Marie Curie.

Work

Aubin 1976 showed that Kähler manifolds ( compact complex manifolds with Kähler metric ) show clearly certain Kähler -Einstein metrics with negative first Chern class, which Eugenio Calabi had suspected. In a way, this theorem generalizes the Uniformisierungstheorem by Henri Poincaré for Riemann surfaces ( Poincaré showed in 1896 that these larger for genus 1 surfaces are negative curvature ) to higher dimensions. At the theorem he worked for his dissertation on nearly twelve years, and led the proof of this theorem in global differential geometry he developed local methods using non-linear partial differential equation of Monge - Ampere type. Shing-Tung Yau treated then shortly thereafter the case of vanishing Chern class, which triggered the Calabi conjecture, for which he received the Fields Medal.

Were also important his work in the context of the problem of Hidehiko Yamabe, who thought to have a proof found that the metric of a Riemannian manifold can be reduced to the form of a metric with constant scalar curvature by conformal transformations 1960. The "proof" of Yamabe turned out to be incorrect ( Neil Trudinger ), because he applied for a occurring in the proof of non-linear partial differential equation of elliptic type variational methods, but in this " non-compact " failed problem. Aubin analyzed the failure of Yamabes evidence and recognized the importance of focusing points of the minimalisierenden functions of the variational problem. His analysis was in the theory of nonlinear partial differential equations important ( Haim Brezis, Louis Nirenberg, Pierre- Louis Lions ). The Yamabe problem was finally solved by Richard Schoen 1984.

Aubin was a member of the Académie des sciences, whose Prix Servant he received in 1982 for 1990 and corresponding since 2003.

Writings

• Nonlinear Analysis on Manifolds. Monge - Ampere Equations, Springer, basic teachings of the mathematical sciences in 1982, ISBN 0,387,907,041th
• A Course in Differential Geometry, American Mathematical Society 2001, ISBN 082182709X.
• Some Nonlinear Problems in Riemannian Geometry, Springer- Verlag 1998, ISBN 3540607528th