We study two known theorems regarding Hermitian matrices: Bellman's principle and Hadamard's theorem. Then we apply them to problems for the complex Monge-Ampère operator. We use Bellman's principle and the theory for plurisubharmonic functions of finite energy to prove a version of subadditivity for the complex Monge-Ampère operator. Then we show how Hadamard's theorem can be extended to polyradial plurisubharmonic functions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-3-3,
author = {Jonas Wiklund},
title = {Matrix inequalities and the complex Monge-Amp\`ere operator},
journal = {Annales Polonici Mathematici},
volume = {83},
year = {2004},
pages = {211-220},
zbl = {1104.32013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-3-3}
}
Jonas Wiklund. Matrix inequalities and the complex Monge-Ampère operator. Annales Polonici Mathematici, Tome 83 (2004) pp. 211-220. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-3-3/