Some regularity theorems for CR mappings
G. P. Balakumar, Kaushal Verma
TL;DR
This paper investigates the smoothness and rigidity of Lipschitz CR mappings between certain hypersurfaces in complex space, establishing conditions under which these mappings are smooth and demonstrating a rigidity property for proper holomorphic mappings.
Contribution
It introduces new regularity results for Lipschitz CR mappings on h-extendible hypersurfaces and proves a rigidity theorem for proper holomorphic mappings from strongly pseudoconvex domains.
Findings
Lipschitz CR mappings are smooth under specific conditions
Proper holomorphic mappings from strongly pseudoconvex domains exhibit rigidity
Regularity results depend on the geometric properties of the hypersurfaces
Abstract
The purpose of this article is to study Lipschitz CR mappings from an -extendible (or semi-regular) hypersurface in . Under various assumptions on the target hypersurface, it is shown that such mappings must be smooth. A rigidity result for proper holomorphic mappings from strongly pseudoconvex domains is also proved.
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Taxonomy
TopicsHolomorphic and Operator Theory · Analytic and geometric function theory · Advanced Banach Space Theory