# Łojasiewicz-Siciak condition for the pluricomplex Green function

Banach Center Publications (2011)

- Volume: 92, Issue: 1, page 197-203
- ISSN: 0137-6934

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topMarta Kosek. "Łojasiewicz-Siciak condition for the pluricomplex Green function." Banach Center Publications 92.1 (2011): 197-203. <http://eudml.org/doc/281833>.

@article{MartaKosek2011,

abstract = {A compact set $K ⊂ ℂ^N$ satisfies Łojasiewicz-Siciak condition if it is polynomially convex and there exist constants B,β > 0 such that
$V_K(z) ≥ B(dist(z,K))^β$ 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).},

author = {Marta Kosek},

journal = {Banach Center Publications},

keywords = {polynomial convexity; plurisubharmonic function; pluricomplex Green function},

language = {eng},

number = {1},

pages = {197-203},

title = {Łojasiewicz-Siciak condition for the pluricomplex Green function},

url = {http://eudml.org/doc/281833},

volume = {92},

year = {2011},

}

TY - JOUR

AU - Marta Kosek

TI - Łojasiewicz-Siciak condition for the pluricomplex Green function

JO - Banach Center Publications

PY - 2011

VL - 92

IS - 1

SP - 197

EP - 203

AB - A compact set $K ⊂ ℂ^N$ satisfies Łojasiewicz-Siciak condition if it is polynomially convex and there exist constants B,β > 0 such that
$V_K(z) ≥ B(dist(z,K))^β$ 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).

LA - eng

KW - polynomial convexity; plurisubharmonic function; pluricomplex Green function

UR - http://eudml.org/doc/281833

ER -

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