Łojasiewicz-Siciak condition for the pluricomplex Green function

Marta Kosek

Marta Kosek

Banach Center Publications, Tome 95 (2011), p. 197-203 / Harvested from The Polish Digital Mathematics Library

Résumé

A compact set $K \subset ℂ^{N}$ satisfies Łojasiewicz-Siciak condition if it is polynomially convex and there exist constants B,β > 0 such that $V_{K} (z) \geq B {(d i s t (z, K))}^{β}$ if dist(z,K) ≤ 1. (LS) Here $V_{K}$ denotes the pluricomplex Green function of the set K. We cite theorems where this condition is necessary in the assumptions and list known facts about sets satisfying inequality (LS).

Publié le : 2011-01-01

Zbl 1229.31002

EUDML-ID : urn:eudml:doc:281833

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-13,
     author = {Marta Kosek},
     title = {\L ojasiewicz-Siciak condition for the pluricomplex Green function},
     journal = {Banach Center Publications},
     volume = {95},
     year = {2011},
     pages = {197-203},
     zbl = {1229.31002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-13}
}

Marta Kosek. Łojasiewicz-Siciak condition for the pluricomplex Green function. Banach Center Publications, Tome 95 (2011) pp. 197-203. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-13/