Montel type theorem for CR mappings between pseudo-Hermitian CR manifolds

HANJIN LEE

doi:10.4134/BKMS.b230540

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2024; 61(5): 1289-1299

Online first article September 24, 2024 Printed September 30, 2024

https://doi.org/10.4134/BKMS.b230540

Montel type theorem for CR mappings between pseudo-Hermitian CR manifolds

Hanjin Lee

Handong Global University

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Abstract

Montel type theorem for CR mappings between strongly linebreak pseudoconvex psuedo-Hermitian CR manifolds satisfying curvature bound conditions is proved. Pre-compactness relies on recently introduced linebreak Schwarz lemma for CR mappings between pseudo-Hermitian manifolds. Smoothness of the limit CR map is proved using CR and holomorphic extensions of CR functions to higher dimensional q-concave CR manifolds.

Keywords: Normal family, pseudo-hermitian manifolds, CR maps

MSC numbers: Primary 32A19, 32V10, 32V25