David Catlin

David William Catlin(born 12 May 1952Rochester, Pennsylvania) is an American mathematician who works on the theory ofseveral complex variables.

Catlin received in 1978 his Ph.D. fromPrinceton UniversityunderJoseph Kohnwith thesisBoundary Behavior of Holomorphic Functions on Weakly Pseudoconvex Domains.^[1]^[2]He is a professor atPurdue 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 byDonald Spencer,a particular case of theNeumann problemfor ${\overline {\partial }}$ ,a non-elliptic boundary value problem.^[3]^[4]

Catlin was an Invited Speaker with talkRegularity of solutions of the ${\overline {\partial }}$ -Neumann problemat theICMin 1986 in Berkeley. In 1989 he received the inauguralStefan Bergman Prize.

His brotherPaul Allen Catlin(1948–1995) also achieved fame as a mathematician, doing research ongraph theory.

Selected publications

Necessary conditions for subellipticity of the ${\overline {\partial }}$ -Neumann problem, Annals of Mathematics, 117, 1983, 147–171doi:10.2307/2006974
Boundary invariants of pseudoconvex domains, Annals of Mathematics 120, 1984, 529–586doi:10.2307/1971087
Subelliptic estimates for the ${\overline {\partial }}$ -Neumann problem on pseudoconvex domains, Annals of Mathematics, 126, 1987, 131–191doi:10.2307/1971347
Estimates of invariant metrics on pseudoconvex domains of dimension two, Mathematische Zeitschrift 200, 1989, 429–466doi: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 toRobert Gunningand 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 ${\overline {\partial }}$ -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 ${\overline {\partial }}$ -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.

References

^David Catlinat theMathematics 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 ${\overline {\partial }}$ -Neumann dans un domaine pseudoconvexe de $\mathrm {\mathbf {C} ^{n}}$ ,d'après D. Catlin,Séminaire Bourbaki 790, 1994/95,
^Tran Vu Khan, University of Padua Seminar 2009/10

External links

David W. Catlin, Mathematics Departrment, Purdue University

[1] David Catlinat theMathematics Genealogy Project

[2] "Boundary Behavior of Holomorphic Functions on Weakly Pseudoconvex Domains".J. Differential Geom.15:605–625. 1981.

[3] Makhlouf Derridj,La sous-ellipticité pour le problème ${\overline {\partial }}$ -Neumann dans un domaine pseudoconvexe de $\mathrm {\mathbf {C} ^{n}}$ ,d'après D. Catlin,Séminaire Bourbaki 790, 1994/95,

[4] Tran Vu Khan, University of Padua Seminar 2009/10

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