معرفی
Jeffrey Case is a Professor of Mathematics at The Pennsylvania State University, affiliated with the Department of Mathematics and the Institute for Gravitation and the Cosmos. He holds a Ph.D. from the University of California, Santa Barbara, awarded in 2010. His research focuses on geometric analysis, conformal and CR geometry, smooth metric measure spaces, and global Riemannian and Lorentzian geometry. His work often explores the interplay between differential geometry, partial differential equations, and mathematical physics.
Key research interests include the study of Einstein and Poincaré-Einstein metrics, renormalized curvature integrals, and the properties of geometric operators such as the GJMS operators and CR Paneitz operator. His recent publications address topics like the Gauss-Bonnet formula for minimal submanifolds, formal self-adjointness of bidifferential operators, and sharp inequalities in trace-free matrix spaces.
Dr. Case’s contributions extend to the development of geometric invariants and the exploration of conformally variational Riemannian invariants. He has investigated boundary value problems, such as the Neumann problem on the Clifford torus, and nonuniqueness results in Yamabe-type problems. His work on the weighted ambient metric and smooth metric measure spaces has advanced understanding of quasi-Einstein metrics and their applications in geometric analysis.
His research also engages with CR geometry, including the study of Q-prime curvature in three dimensions and the CR Paneitz operator’s role in stability questions. He frequently employs techniques from global analysis, spectral geometry, and geometric measure theory in his investigations.
