On the local pseudoconvexity of certain analytic families of ℂ

2019/05/24 by Takeo Ohsawa · 1 citation
Mathematics · #Analytic and geometric function theory #Holomorphic and Operator Theory #Advanced Banach Space Theory

paper · pdf · doi:10.5802/aif.3226

openalex publication_date 2019/05/24 · openalex created_date 2019/05/29 · openalex updated_date 2026/07/02

Abstract

For a class of weakly 1-complete <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℂ</mml:mi> </mml:math> bundles over compact Riemann surfaces, for which canonical plurisubharmonic exhaustion functions on the total spaces are known, some cases are described where such functions can be extended to a plurisubharmonic exhaustion function on analytic families of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℂ</mml:mi> </mml:math> bundles. The nonextendable cases are also discussed.

Citations

• Bemerkenswerte pseudokonvexe Mannigfaltigkeiten
• Sur les fonctions analytiques de plusieurs variables

Cited by

• Function of several complex variables [wikipedia]

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