Geodesics in the Space of m-Subharmonic Functions With Bounded Energy

被引：1

作者：

Ahag, Per ^{[1
]}

Czyz, Rafal ^{[2
]}

机构：

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

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

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2023年 / 2023卷 / 12期

关键词：

COMPLEX MONGE-AMPERE; DIRICHLET PROBLEM; METRIC GEOMETRY; WEAK SOLUTIONS; ENVELOPES; EQUATIONS;

D O I：

10.1093/imrn/rnac129

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

With inspiration from the Kahler geometry, we introduce a metric structure on the energy class, epsilon(1,m), of m-subharmonic functions with bounded energy and show that it is complete. After studying how the metric convergence relates to the accepted convergences in this Caffarelli-Nirenberg-Spruck model, we end by constructing geodesics in a subspace of our complete metric space.

引用

页码：10115 / 10155

页数：41

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