A new proof of Kiselman's minimum principle for plurisubharmonic functions

Deng, Fusheng; Wang, Zhiwei; Zhang, Liyou; Zhou, Xiangyu

doi:10.1016/j.crma.2019.04.006

Complex analysis/Analytic geometry

A new proof of Kiselman's minimum principle for plurisubharmonic functions
[Une nouvelle démonstration du principe du minimum de Kiselman pour les fonctions pluri-sous-harmoniques]

Présenté par : Jean-Pierre Demailly

Deng, Fusheng ¹ ; Wang, Zhiwei ² ; Zhang, Liyou ³ ; Zhou, Xiangyu ^1,⁴

¹ School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
² School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, PR China
³ School of Mathematical Sciences, Capital Normal University, Beijing, 100048, PR China
⁴ Institute of Mathematics, AMSS, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, PR China

Comptes Rendus. Mathématique, Tome 357 (2019) no. 4, pp. 345-348.

Résumé
Abstract

Nous donnons une nouvelle démonstration du principe du minimum de Kiselman pour les fonctions pluri-sous-harmoniques. Elle s'inspire de la régularisation des fonctions pluri-sous-harmoniques de Demailly, en utilisant le théorème d'extension d'Ohsawa–Takegoshi.

We give a new proof of Kiselman's minimum principle for plurisubharmonic functions, inspired by Demailly's regularization of plurisubharmonic functions by using Ohsawa–Takegoshi's extension theorem.

Reçu le : 2019-01-02
Accepté le : 2019-04-12
Publié le : 2019-04-01

DOI : 10.1016/j.crma.2019.04.006

Affiliations des auteurs :

Deng, Fusheng ¹ ; Wang, Zhiwei ² ; Zhang, Liyou ³ ; Zhou, Xiangyu ^{1, 4}

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     title = {A new proof of {Kiselman's} minimum principle for plurisubharmonic functions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {345--348},
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Deng, Fusheng; Wang, Zhiwei; Zhang, Liyou; Zhou, Xiangyu. A new proof of Kiselman's minimum principle for plurisubharmonic functions. Comptes Rendus. Mathématique, Tome 357 (2019) no. 4, pp. 345-348. doi : 10.1016/j.crma.2019.04.006. http://www.numdam.org/articles/10.1016/j.crma.2019.04.006/

Bibliographie
Cité par

[1] Berndtsson, B. Prekopa's theorem and Kiselman's minimum principle for plurisubharmonic functions, Math. Ann., Volume 312 (1998), pp. 785-792

[2] Demailly, J.-P. Regularization of closed positive currents and intersection theory, J. Algebraic Geom., Volume 1 (1992) no. 3, pp. 361-409

[3] Deng, F.; Wang, Z.; Zhang, L.; Zhou, X. New characterization of plurisubharmonic functions and positivity of direct image sheaves | arXiv

[4] Deng, F.; Zhang, H.; Zhou, X. Positivity of direct images of positively curved volume forms, Math. Z., Volume 278 (2014), pp. 347-362

[5] Deng, F.; Zhang, H.; Zhou, X. Positivity of character subbundles and minimumprinciple for noncompact group actions, Math. Z., Volume 286 (2017), pp. 431-442

[6] Kiselman, C. The partial Legendre transformation for plurisubharmonic functions, Invent. Math., Volume 49 (1978) no. 2, pp. 137-148

[7] Ohsawa, T.; Takegoshi, K. On the extension of $L^{2}$ holomorphic functions, Math. Z., Volume 195 (1987) no. 2, pp. 197-204

Cité par Sources :

^☆ The authors are partially supported respectively by NSFC grants [NSFC-11871451], [NSFC-11701031], [NSFC-11671270], [NSFC-11688101]. The second author was partially supported by the Fundamental Research Funds for the Central Universities.