{"title":"Rooftop envelopes and residual plurisubharmonic functions","authors":"A. Rashkovskii","doi":"10.4064/ap210624-12-11","DOIUrl":null,"url":null,"abstract":"Given a negative plurisubharmonic function φ in a bounded pseudoconvex domain of C, we introduce and study its residual function gφ determined by the asymptotic behavior of φ near its singularity points, both inside the domain and on its boundary. For certain choices of φ, the function gφ coincides with different versions of pluricomplex Green functions. The considerations are motivated by a problem on when two given plurisubharmonic functions can be connected by a plurisubharmonic geodesic. Mathematic Subject Classification: 32U05, 32U15, 32U35, 32W20","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"23 5","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2021-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Polonici Mathematici","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/ap210624-12-11","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 5
Abstract
Given a negative plurisubharmonic function φ in a bounded pseudoconvex domain of C, we introduce and study its residual function gφ determined by the asymptotic behavior of φ near its singularity points, both inside the domain and on its boundary. For certain choices of φ, the function gφ coincides with different versions of pluricomplex Green functions. The considerations are motivated by a problem on when two given plurisubharmonic functions can be connected by a plurisubharmonic geodesic. Mathematic Subject Classification: 32U05, 32U15, 32U35, 32W20
期刊介绍：
Annales Polonici Mathematici is a continuation of Annales de la Société Polonaise de Mathématique (vols. I–XXV) founded in 1921 by Stanisław Zaremba.
The journal publishes papers in Mathematical Analysis and Geometry. Each volume appears in three issues.
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