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
收藏
页码：10115 / 10155
页数：41
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