to satisfy certain orthogonality constraints. Such results are naturally applicable to many problems in the field of geometric analysis. Aubin considered the Yamabe problem on conformal deformation to constant scalar curvature, which Yamabe had reduced to a problem in the calculus of variations. Following prior work of Neil Trudinger, Aubin was able to resolve the problem in high dimensions under the condition that the Weyl curvature is nonzero at some point. The key of Aubin's analysis is essentially local, with an estimate on the geometry of the Green's function based on the Weyl curvature. The more subtle case of locally conformally flat manifolds, along with the low-dimensional case, was later established by Richard Schoen as an application of Schoen and Yau's positive mass theorem. All of the results outlined here, along with many others, were absorbed into Aubin's book Some Nonlinear Problems in Riemannian Geometry, which has become a basic part of the research literature. Major Publications Articles. Aubin was the author of around sixty research papers. The following, among the best-known, are outlined above. Books Expansion of: References External links Obituary on the SMF Gazette 1942 births 2009 deaths 20th-century French mathematicians Differential geometers Members of the French Academy of Sciences Institute for Advanced Study visiting scholars École Polytechnique alumni 21st-century French mathematicians