Jerry L. Kazdan (born 1945) is an American mathematician specializing in differential geometry and nonlinear partial differential equations. He is noted for his contributions to the prescribed scalar curvature problem, particularly the Kazdan–Warner theorem, which characterizes which functions can arise as the scalar curvature of a Riemannian metric on a given manifold.
Early life and education
Kazdan earned his Bachelor of Science degree in mathematics from the University of Michigan in 1967. He completed his Ph.D. in mathematics at the University of Chicago in 1970 under the supervision of Shiing-Shen Chern, with a dissertation titled “Prescribing Curvature on Compact Manifolds.”
Academic career
After receiving his doctorate, Kazdan held a post‑doctoral position at the Institute for Advanced Study. He joined the faculty of the University of Pennsylvania in 1972, where he advanced from assistant professor to full professor. In 2001, he moved to the University of Utah, where he served as a professor of mathematics until his retirement in 2015, after which he was granted emeritus status.
Research contributions
Kazdan’s research focuses on the interplay between geometry and analysis. His most influential work, carried out jointly with F. W. Warner, established necessary and sufficient conditions for a smooth function on a compact manifold to be realized as the scalar curvature of some smooth Riemannian metric. This result, known as the Kazdan–Warner theorem, has become a foundational component of geometric analysis and has spurred extensive subsequent research on curvature prescription problems.
Other notable contributions include:
- Development of techniques for solving nonlinear elliptic partial differential equations arising in geometry.
- Results on the existence of metrics with constant scalar curvature on manifolds of various topological types.
- Collaborative work on the Yamabe problem and related conformal deformation issues.
Publications
Kazdan has authored and co‑authored numerous research articles and several influential monographs, including:
- Prescribing Curvatures (American Mathematical Society, 1995).
- The Scalar Curvature Equation on Compact Manifolds (with F. Warner, Journal of Differential Geometry, 1975).
Awards and honors
- Sloan Research Fellowship (1974).
- Fellow of the American Mathematical Society (2012).
Professional service
Kazdan has served on editorial boards for journals such as Calculus of Variations and Partial Differential Equations and Geometriae Dedicata. He has also been a frequent invited speaker at international conferences on geometric analysis.
Personal life
Details regarding Kazdan’s personal life are not widely publicized.
Legacy
The Kazdan–Warner theorem remains a central result in differential geometry, influencing both theoretical developments and applications in mathematical physics. Kazdan’s work continues to be cited extensively in research on curvature prescription and geometric PDEs.