Convexity of sublevel sets of plurisubharmonic extremal functions
Finnur Lárusson; Patrice Lassere; Ragnar Sigurdsson
Annales Polonici Mathematici (1998)
- Volume: 68, Issue: 3, page 267-273
- ISSN: 0066-2216
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topFinnur Lárusson, Patrice Lassere, and Ragnar Sigurdsson. "Convexity of sublevel sets of plurisubharmonic extremal functions." Annales Polonici Mathematici 68.3 (1998): 267-273. <http://eudml.org/doc/270205>.
@article{FinnurLárusson1998,
abstract = {Let X be a convex domain in ℂⁿ and let E be a convex subset of X. The relative extremal function $u_\{E,X\}$ for E in X is the supremum of the class of plurisubharmonic functions v ≤ 0 on X with v ≤ -1 on E. We show that if E is either open or compact, then the sublevel sets of $u_\{E,X\}$ are convex. The proof uses the theory of envelopes of disc functionals and a new result on Blaschke products.},
author = {Finnur Lárusson, Patrice Lassere, Ragnar Sigurdsson},
journal = {Annales Polonici Mathematici},
keywords = {plurisubharmonic; relative extremal function; convex; disc functional; envelope; Blaschke product; plurisubharmonic relative extremal function; disc functionals},
language = {eng},
number = {3},
pages = {267-273},
title = {Convexity of sublevel sets of plurisubharmonic extremal functions},
url = {http://eudml.org/doc/270205},
volume = {68},
year = {1998},
}
TY - JOUR
AU - Finnur Lárusson
AU - Patrice Lassere
AU - Ragnar Sigurdsson
TI - Convexity of sublevel sets of plurisubharmonic extremal functions
JO - Annales Polonici Mathematici
PY - 1998
VL - 68
IS - 3
SP - 267
EP - 273
AB - Let X be a convex domain in ℂⁿ and let E be a convex subset of X. The relative extremal function $u_{E,X}$ for E in X is the supremum of the class of plurisubharmonic functions v ≤ 0 on X with v ≤ -1 on E. We show that if E is either open or compact, then the sublevel sets of $u_{E,X}$ are convex. The proof uses the theory of envelopes of disc functionals and a new result on Blaschke products.
LA - eng
KW - plurisubharmonic; relative extremal function; convex; disc functional; envelope; Blaschke product; plurisubharmonic relative extremal function; disc functionals
UR - http://eudml.org/doc/270205
ER -
References
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