The Geometry of m-Hyperconvex Domains

被引：20

作者：

Ahag, Per ^{[1
]}

Czyz, Rafal ^{[2
]}

Hed, Lisa ^{[1
]}

机构：

[1] Umea Univ, Dept Math & Math Stat, S-90187 Umea, Sweden

[2] Jagiellonian Univ, Fac Math & Comp Sci, Lojasiewicza 6, PL-30348 Krakow, Poland

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2018年 / 28卷 / 04期

关键词：

Barrier function; Caffarelli-Nirenberg-Spruck model; Exhaustion function; m-subharmonic function; Jensen measure; PLURISUBHARMONIC-FUNCTIONS; PSEUDOCONVEX DOMAINS; POTENTIAL-THEORY; BOUNDARY-VALUES; JENSEN MEASURES; LELONG NUMBER; APPROXIMATION; DEFINITION; INEQUALITY; CONVEXITY;

D O I：

10.1007/s12220-017-9957-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the geometry of m-regular domains within the Caffarelli-Nirenberg-Spruck model in terms of barrier functions, envelopes, exhaustion functions, and Jensen measures. We prove among other things that every m-hyperconvex domain admits an exhaustion function that is negative, smooth, strictly m-subharmonic, and has bounded m-Hessian measure.

引用

页码：3196 / 3222

页数：27

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