Deformations of Strongly Pseudoconvex Domains

2010/04/21 by Steven G. Krantz, Krantz, Steven G.
Mathematics · #32E05 #32E40 #32T05 #32T15 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV #msc:32E05 #msc:32E40 #msc:32T05 #msc:32T15

paper · pdf · doi:10.48550/arxiv.1004.3780

arxiv created 2010/04/21 · openalex publication_date 2010/04/21 · arxiv updated 2010/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that two smoothly bounded, strongly pseudoconvex domains which are diffeomorphic may be smoothly deformed into each other, with all intermediate domains being strongly pseudoconvex. This result relates to Lempert's ideas about Kobayashi extremal discs, and also has intrinsic interest.

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