Catlin received in 1978 his Ph.D. from Princeton University under Joseph Kohn with thesis Boundary Behavior of Holomorphic Functions on Weakly Pseudoconvex Domains. He is a professor at Purdue University.
He solved a boundary behavior problem of complex analysis in several variables, on which his teacher Kohn worked in detail and which was originally formulated by Donald Spencer, a particular case of the Neumann problem for , a non-elliptic boundary value problem.
- Necessary conditions for subellipticity of the -Neumann problem, Annals of Mathematics, 117, 1983, 147–171 doi:10.2307/2006974
- Boundary invariants of pseudoconvex domains, Annals of Mathematics 120, 1984, 529–586 doi:10.2307/1971087
- Subelliptic estimates for the -Neumann problem on pseudoconvex domains, Annals of Mathematics, 126, 1987, 131–191 doi:10.2307/1971347
- Estimates of invariant metrics on pseudoconvex domains of dimension two, Mathematische Zeitschrift 200, 1989, 429–466 doi:10.1007/BF01215657
- as editor with Thomas Bloom, John P. D'Angelo, Yum-Tong Siu: Modern methods in complex analysis, Annals of Mathematics Studies 137, Princeton University Press 1995 (dedicated to Robert Gunning and Joseph Kohn)
- with J. P. D'Angelo: A stabilization theorem for Hermitian forms and applications to holomorphic mappings, arXiv preprint math/9511201, 1995
- Global regularity of the -Neumann problem, in: Complex analysis of several variables, Proc. Symp. Pure Math. Vol. 41, AMS, 1984, 39–49
- Necessary conditions for subellipticity and hypoellipticity for the -Neumann problem on pseudoconvex domains, in: Recent Developments in Several Complex Variables (John E. Fornæss, ed.), Annals of Mathematics Studies Vol. 100, 2016, 93–100.
- David Catlin at the Mathematics Genealogy Project
- "Boundary Behavior of Holomorphic Functions on Weakly Pseudoconvex Domains". J. Differential Geom. 15: 605–625. 1981.
- Makhlouf Derridj, La sous-ellipticité pour le problème -Neumann dans un domaine pseudoconvexe de , d'après D. Catlin, Séminaire Bourbaki 790, 1994/95,
- Tran Vu Khan, University of Padua Seminar 2009/10