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on
Riemannian manifolds. He established Riemannian formulations of many classical results for Sobolev spaces, such as the equivalence of various definitions, the density of various subclasses of functions, and the standard embedding theorems. In one of Aubin's best-known works, the analysis of the
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proved the more powerful Calabi conjecture, which concerns the general problem of prescribing the Ricci curvature of a Kähler metric, via non-variational methods. As such, the existence of Kähler–Einstein metrics with negative first Chern class is often called the
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567:"Meilleures constantes dans le théorème d'inclusion de Sobolev et un théorème de Fredholm non linéaire pour la transformation conforme de la courbure scalaire"
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135:(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
289:, Aubin later proved improvements of the optimal constants when the functions are assumed to satisfy certain orthogonality constraints.
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to constant scalar curvature, which Yamabe had reduced to a problem in the calculus of variations. Following prior work of
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Aubin, Thierry (1976c). "Équations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire".
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is nonzero at some point. The key of Aubin's analysis is essentially local, with an estimate on the geometry of the
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can be deformed to positive Ricci curvature, provided that its Ricci curvature is strictly positive at one point.
346:. Aubin was the author of around sixty research papers. The following, among the best-known, are outlined above.
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143:. His fundamental contributions to the theory of the Yamabe equation led, in conjunction with results of
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Aubin, Thierry (1978). "Équations du type Monge–Ampère sur les variétés kählériennes compactes".
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183:. The latter result, established by Yau, provides the largest class of known examples of compact
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All of the results outlined here, along with many others, were absorbed into Aubin's book
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Aubin, Thierry (1976a). "Espaces de
Sobolev sur les variétés riemanniennes".
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674:. Grundlehren der mathematischen Wissenschaften. Vol. 252. New York:
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manifolds, along with the low-dimensional case, was later established by
503:"Équations du type Monge–Ampère sur les variétés kähleriennes compactes"
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Such results are naturally applicable to many problems in the field of
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Aubin made a number of fundamental contributions to the study of
225:. Furthermore, he proved that a Riemannian metric of nonnegative
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can be conformally rescaled to produce a manifold of constant
335:, which has become a basic part of the research literature.
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Nonlinear analysis on manifolds. Monge–Ampère equations
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Nonlinear analysis on manifolds. Monge–Ampère equations
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In the same year, Aubin introduced an approach to the
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Institute for
Advanced Study: A Community of Scholars
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based on the Weyl curvature. The more subtle case of
244:. Later, in 1976, Aubin established the existence of
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was carried out. Along with similar results for the
187:. Aubin was the first mathematician to propose the
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508:Comptes Rendus de l'Académie des Sciences, Série A
427:"Problèmes isopérimétriques et espaces de Sobolev"
851:This book is an expansion of Aubin's prior book
925:Institute for Advanced Study visiting scholars
621:. Springer Monographs in Mathematics. Berlin:
619:Some nonlinear problems in Riemannian geometry
333:Some Nonlinear Problems in Riemannian Geometry
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473:Journal de Mathématiques Pures et Appliquées
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920:Members of the French Academy of Sciences
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265:. After learning Yau's techniques from
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324:as an application of Schoen and Yau's
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353:"MĂ©triques riemanniennes et courbure"
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210:In 1970, Aubin established that any
194:Aubin was a visiting scholar at the
538:Bulletin des Sciences Mathématiques
398:Bulletin des Sciences Mathématiques
217:of dimension larger than two has a
935:21st-century French mathematicians
910:20th-century French mathematicians
179:, a result closely related to the
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723:A course in differential geometry
109:Pierre and Marie Curie University
729:. Vol. 27. Providence, RI:
432:Journal of Differential Geometry
358:Journal of Differential Geometry
74:
29:
727:Graduate Studies in Mathematics
198:in 1979. He was elected to the
572:Journal of Functional Analysis
141:partial differential equations
1:
873:Mathematics Genealogy Project
731:American Mathematical Society
177:Kähler–Einstein metrics
586:10.1016/0022-1236(79)90052-1
256:is negative. Independently,
196:Institute for Advanced Study
951:
930:École Polytechnique alumni
287:Moser–Trudinger inequality
189:Cartan–Hadamard conjecture
684:10.1007/978-1-4612-5734-9
631:10.1007/978-3-662-13006-3
283:Sobolev embedding theorem
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37:(photo by George Bergman)
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501:Aubin, Thierry (1976d).
425:Aubin, Thierry (1976b).
318:locally conformally flat
281:optimal constant in the
721:Aubin, Thierry (2001).
670:Aubin, Thierry (1982).
617:Aubin, Thierry (1998).
565:Aubin, Thierry (1979).
351:Aubin, Thierry (1970).
296:. Aubin considered the
271:Jean-Pierre Bourguignon
246:Kähler–Einstein metrics
915:Differential geometers
446:10.4310/jdg/1214433725
372:10.4310/jdg/1214429638
242:calculus of variations
167:, he also showed that
326:positive mass theorem
302:conformal deformation
200:Académie des sciences
35:Thierry Aubin in 1976
171:with negative first
151:, to a proof of the
16:French mathematician
157:Riemannian manifold
137:Riemannian geometry
791:2013-01-06 at the
476:. Neuvième Série.
339:Major Publications
294:geometric analysis
236:, in the field of
185:Einstein manifolds
121:André Lichnerowicz
263:Aubin–Yau theorem
254:first Chern class
234:Calabi conjecture
219:Riemannian metric
181:Calabi conjecture
153:Yamabe Conjecture
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89:Scientific career
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161:scalar curvature
155:: every compact
116:Doctoral advisor
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322:Richard Schoen
310:Weyl curvature
306:Neil Trudinger
298:Yamabe problem
278:Sobolev spaces
258:Shing-Tung Yau
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163:. Along with
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540:. 2e SĂ©rie.
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400:. 2e SĂ©rie.
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267:Jerry Kazdan
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221:of negative
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105:Institutions
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63:(2009-03-21)
905:2009 deaths
900:1942 births
828:Aubin 1976a
804:Aubin 1976d
99:Mathematics
70:Nationality
894:Categories
840:Aubin 1979
816:Aubin 1978
773:References
765:0966.53001
710:0512.53044
657:0896.53003
603:0411.46019
558:0374.53022
529:0333.53040
494:0336.53033
463:0371.46011
418:0328.46030
389:0212.54102
240:, via the
53:6 May 1942
49:1942-05-06
202:in 2003.
145:Trudinger
878:Obituary
789:Archived
344:Articles
206:Research
885:Gazette
880:on the
871:at the
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95:Fields
82:France
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743:ISBN
688:ISBN
635:ISBN
147:and
58:Died
43:Born
882:SMF
761:Zbl
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
