{"title":"On the Edrei–Goldberg–Ostrovskii Theorem for Minimal Surfaces","authors":"A. Kowalski, I. I. Marchenko","doi":"10.1007/s10476-023-0230-6","DOIUrl":null,"url":null,"abstract":"<div><p>This paper is devoted to the development of Beckenbach’s theory of the meromorphic minimal surfaces. We consider the relationship between the number of separated maximum points of a meromorphic minimal surface and the Baernstein’s <i>T</i>*-function. The results of Edrei, Goldberg, Heins, Ostrovskii, Wiman are generalized. We also give examples showing that the obtained estimates are sharp.</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":"49 3","pages":"807 - 823"},"PeriodicalIF":0.6000,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis Mathematica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10476-023-0230-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
This paper is devoted to the development of Beckenbach’s theory of the meromorphic minimal surfaces. We consider the relationship between the number of separated maximum points of a meromorphic minimal surface and the Baernstein’s T*-function. The results of Edrei, Goldberg, Heins, Ostrovskii, Wiman are generalized. We also give examples showing that the obtained estimates are sharp.
期刊介绍：
Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx).
The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx).
The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.
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