Abbas Bahri (1 January 1955 – 10 January 2016) was a Tunisian mathematician best known for foundational work in the calculus of variations and its applications. He held a professorship at Rutgers University and received several international honors, including the Fermat Prize and the Langevin Prize. For a concise biographical overview see biographical sources.
Areas of work
Bahri's research bridged several closely related fields. His principal interests included the calculus of variations, where one studies functionals and their extrema; nonlinear partial differential equations (PDEs), which describe many physical and geometric phenomena; and differential geometry, which provides the geometric framework for many variational problems (differential geometry). His approach combined analytic techniques with topological and geometric insight.
Key contribution: critical points at infinity
Bahri introduced and developed the method of "critical points at infinity," a conceptual and technical framework to handle variational problems that lack compactness. When minimizing sequences fail to converge because they "escape" in function space, these escapes can often be described as limiting objects that behave like critical points located at infinity. By treating those limiting behaviours as part of a generalized Morse theory, Bahri made it possible to obtain existence and multiplicity results in settings where standard compactness assumptions break down. This idea has been influential in studying geometric PDEs and variational equations.
His methods were applied to a variety of nonlinear problems, including existence theorems for solutions to elliptic equations arising in geometry and physics, and to questions about prescribing curvature on manifolds. The conceptual clarity of treating noncompact behavior as structured objects opened new avenues for combining topology with analysis.
Career, recognition and legacy
Bahri served as a professor at Rutgers University, where he supervised research and continued to publish on analytic and geometric problems. He was awarded major prizes such as the Fermat Prize and the Langevin Prize in recognition of his contributions. Colleagues remember him for introducing tools that remain part of the standard toolkit in modern variational analysis.
- Main research areas: calculus of variations, partial differential equations, and differential geometry.
- Notable idea: method of critical points at infinity, used to overcome loss of compactness.
- Honors: recipient of international awards including the Fermat and Langevin prizes.
Abbas Bahri died on 10 January 2016 after a long illness. His work continues to influence researchers working at the interface of analysis, geometry, and topology, and his techniques are taught as part of advanced courses dealing with variational methods and nonlinear elliptic equations.