Thierry Aubin

Thierry Aubin
Name	Thierry Aubin
Birth date	1932
Birth place	Paris
Death date	2016
Occupation	Mathematician
Known for	Work in Riemannian geometry, Yamabe problem, nonlinear partial differential equations
Awards	Prix Servant, FNRS Prix

Thierry Aubin was a French mathematician noted for foundational contributions to Riemannian geometry and global analysis, particularly for advances on the Yamabe problem and existence results for nonlinear elliptic equations on compact manifolds. His research influenced subsequent developments in geometric analysis, impacting work by scholars in PDE-centered institutions and research groups across France, United States, and Japan. Aubin's results connected techniques from variational methods, Sobolev space theory, and curvature prescription problems, shaping modern approaches to conformal geometry and scalar curvature questions.

Early life and education

Born in Paris in 1932, Aubin completed early schooling in the French capital before entering higher education at the École Normale Supérieure (Paris). He studied under mentors linked to the French mathematical tradition including scholars associated with Henri Cartan-era circles and the postwar revival of CNRS research. Aubin obtained his doctorate at a time when problems in Riemannian geometry and nonlinear analysis were undergoing rapid development, influenced by earlier work of André Lichnerowicz and contemporaries such as Jean-Pierre Serre and Laurent Schwartz.

Academic career

Aubin held positions at prominent French institutions, including the Université Paris-Sud and affiliations with CNRS research units. He taught and supervised graduate students who later joined faculties at institutions like Université de Strasbourg, Université de Grenoble, and international centers such as Princeton University and Massachusetts Institute of Technology. Through collaborations and conferences he engaged with mathematicians from Italy, Germany, United Kingdom, and United States, contributing to networks that included participants from the International Congress of Mathematicians and symposia at Institut Henri Poincaré.

Contributions to differential geometry and global analysis

Aubin made seminal contributions to problems at the intersection of Riemannian geometry and nonlinear partial differential equations. He established key existence theorems for conformal deformations of metrics to prescribe scalar curvature on compact manifolds, building on the work of Hidehiko Yamabe, Neil Trudinger, and James M. K. Weaver-style variational techniques. His analyses employed sharp estimates in Sobolev inequalities and compactness results connected to the concentration-compactness principle later formalized by Pierre-Louis Lions. Aubin proved important embedding theorems in the spirit of the Rellich–Kondrachov theorem adapted to geometric settings and clarified the role of Green's functions and blow-up analysis in elliptic equations on manifolds.

He contributed to the conceptual framework used to tackle the Yamabe problem by providing existence results under curvature and topological constraints and introducing methods to handle lack of compactness arising from conformal invariance. Aubin's work influenced subsequent resolutions of the full Yamabe conjecture by researchers such as Richard Schoen and provided tools later used in studies by Michael Struwe and Ovidiu Savin. His techniques proved applicable to problems in the study of eigenvalue estimates related to the Laplacian on Riemannian manifolds and to functional inequalities central to geometric flows studied by scholars like Richard Hamilton and Grigori Perelman.

Selected publications and theorems

Aubin authored influential monographs and papers that became standard references in geometric analysis. His major publications include texts presenting existence theorems for nonlinear elliptic equations on compact manifolds, treatments of Sobolev spaces on manifolds, and expositions of variational methods applied to geometry. Notable theorems associated with his name concern sharp constants in Sobolev-type inequalities on manifolds, existence for conformal scalar curvature equations under specific sign or compactness conditions, and compactness criteria for sequences of metrics with bounded energy. His writings influenced later rigorous treatments by mathematicians such as Emmanuel Hebey, Marcel Berger, Thierry Coulhon, and Michel Ledoux.

Awards and honors

During his career Aubin received national recognition including prizes awarded by French scientific societies. He was a recipient of distinctions such as the Prix Servant and honors conferred by institutions like Académie des sciences and research funding bodies including CNRS. He was invited to present at major conferences and served on editorial boards of leading journals in analysis and geometry, participating in academic governance at universities and national academies that include connections to Collège de France networks.

Personal life and legacy

Aubin maintained close ties with the French mathematical community and mentored a generation of analysts and geometers who continued work on conformal geometry, geometric PDE, and global analysis. His legacy endures through his monographs, theorems used in subsequent resolutions of longstanding conjectures, and the influence his students carried into faculties worldwide, including roles at University of California, Berkeley, Université Paris-Sud, ETH Zurich, and University of Tokyo. Posthumous recognitions and conferences commemorated his impact alongside celebrations of related milestones in geometric analysis and the broader mathematical traditions of France.

Category:French mathematicians Category:1932 births Category:2016 deaths