{"title":"Ramification and unicity theorems for Gauss maps of complete space-like stationary surfaces in four-dimensional Lorentz-Minkowski space","authors":"Li Ou","doi":"10.1016/j.difgeo.2025.102238","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we investigate value distribution properties for Gauss maps of space-like stationary surfaces in four-dimensional Lorentz-Minkowski space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span>, focusing on aspects such as the total weight of totally ramified values and unicity properties. We obtain not only general conclusions analogous to those in four-dimensional Euclidean space, but also results for space-like stationary surfaces with rational graphical Gauss image, which is an extension of degenerate space-like stationary surfaces.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"99 ","pages":"Article 102238"},"PeriodicalIF":0.6000,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Geometry and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0926224525000130","RegionNum":4,"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
In this paper, we investigate value distribution properties for Gauss maps of space-like stationary surfaces in four-dimensional Lorentz-Minkowski space , focusing on aspects such as the total weight of totally ramified values and unicity properties. We obtain not only general conclusions analogous to those in four-dimensional Euclidean space, but also results for space-like stationary surfaces with rational graphical Gauss image, which is an extension of degenerate space-like stationary surfaces.
期刊介绍：
Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.
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