Thierry Aubin (nonfiction)

Thierry Aubin.

Thierry Aubin (6 May 1942 – 21 March 2009) was a French mathematician who worked at the Centre de Mathématiques de Jussieu, and was a leading expert on Riemannian geometry and non-linear partial differential equations. His fundamental contributions to the theory of the Yamabe equation led, in conjunction with results of Neil Trudinger and Richard Schoen, to a proof of the Yamabe Conjecture: every compact Riemannian manifold can be conformally rescaled to produce a manifold of constant scalar curvature. Along with Shing-Tung Yau, he also showed that Kähler manifolds with negative first Chern classes always admit Kähler–Einstein metrics, a result closely related to the Calabi conjecture. The latter result provides the largest class of known examples of compact Einstein manifolds. Aubin was the first mathematician to propose the Cartan–Hadamard conjecture.

Aubin was a visiting scholar at the Institute for Advanced Study in 1979.[1] He was elected to the Académie des sciences in 2003.

Publications

• Nonlinear Analysis on Manifolds. Monge–Ampère Equations ISBN 0-387-90704-1
• A Course in Differential Geometry ISBN 0-8218-2709-X
• Some Nonlinear Problems in Riemannian Geometry ISBN 3-540-60752-8

References

• Institute for Advanced Study: A Community of Scholars Archived 2013-01-06 at the Wayback Machine

External links

• Thierry Aubin at the Mathematics Genealogy Project
• Obituary on the SMF Gazette

• Calabi conjecture (nonfiction) - a conjecture about the existence of certain "nice" Riemannian metrics on certain complex manifolds, made by Eugenio Calabi (1954, 1957) and proved by Shing-Tung Yau (1977, 1978).
• Cartan–Hadamard conjecture (nonfiction) - a fundamental problem in Riemannian geometry and Geometric measure theory which states that the classical isoperimetric inequality may be generalized to spaces of nonpositive sectional curvature, known as Cartan–Hadamard manifolds. The conjecture, which is named after French mathematicians Élie Cartan and Jacques Hadamard, may be traced back to work of André Weil in 1926. Informally, the conjecture states that negative curvature allows regions with a given perimeter to hold more volume. This phenomenon manifests itself in nature through corrugations on coral reefs, or ripples on a petunia flower, which form some of the simplest examples of non-positively curved spaces.
• Chern class (nonfiction) - characteristic classes associated with complex vector bundles.
• Einstein manifold (nonfiction) - a Riemannian or pseudo-Riemannian differentiable manifold whose Ricci tensor is proportional to the metric. They are named after Albert Einstein because this condition is equivalent to saying that the metric is a solution of the vacuum Einstein field equations (with cosmological constant), although both the dimension and the signature of the metric can be arbitrary, thus not being restricted to the four-dimensional Lorentzian manifolds usually studied in general relativity.
• Kähler–Einstein metric (nonfiction) - a Riemannian metric that is both a Kähler metric and an Einstein metric. A manifold is said to be Kähler–Einstein if it admits a Kähler–Einstein metric. The most important special case of these are the Calabi–Yau manifolds, which are Kähler and Ricci-flat.
• Kähler manifold (nonfiction) - a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure. The concept was first studied by Jan Arnoldus Schouten and David van Dantzig in 1930, and then introduced by Erich Kähler in 1933. The terminology has been fixed by André Weil.
• Partial differential equation (nonfiction) -
• Riemannian geometry (nonfiction) -
• Scalar curvature (nonfiction) - the simplest curvature invariant of a Riemannian manifold.
• Yamabe problem (nonfiction) - in differential geometry concerns the existence of Riemannian metrics with constant scalar curvature, taking its name from mathematician Hidehiko Yamabe.