Complex analysis/Analytic geometry
A new proof of Kiselman's minimum principle for plurisubharmonic functions
Comptes Rendus. Mathématique, Volume 357 (2019) no. 4, pp. 345-348.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2019.04.006
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
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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, Volume 357 (2019) no. 4, pp. 345-348. doi : 10.1016/j.crma.2019.04.006. http://archive.numdam.org/articles/10.1016/j.crma.2019.04.006/

[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 L2 holomorphic functions, Math. Z., Volume 195 (1987) no. 2, pp. 197-204

Cited by 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.