# 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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