{"title":"RAMIFICATION OVER HYPERSURFACES LOCATED IN SUBGENERAL POSITION OF THE GAUSS MAP OF COMPLETE MINIMAL SURFACES WITH FINITE TOTAL CURVATURE","authors":"D. D. Thai, Pham Duc Thoan","doi":"10.2206/KYUSHUJM.72.253","DOIUrl":null,"url":null,"abstract":"The first aim of this paper is to show the second main theorem for holomorphic maps from a compact Riemann surface into the complex projective space which is ramified over hypersurfaces in subgeneral position. We then use it to study the ramification over hypersurfaces of the generalized Gauss map of complete regular minimal surfaces in Rm with finite total curvature, sharing hypersurfaces in subgeneral position. The results generalize our previous results [Thai and Thoan, Vietnam J. Math. 2017, doi:10.1007/s10013-017-0259-6].","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2206/KYUSHUJM.72.253","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2206/KYUSHUJM.72.253","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The first aim of this paper is to show the second main theorem for holomorphic maps from a compact Riemann surface into the complex projective space which is ramified over hypersurfaces in subgeneral position. We then use it to study the ramification over hypersurfaces of the generalized Gauss map of complete regular minimal surfaces in Rm with finite total curvature, sharing hypersurfaces in subgeneral position. The results generalize our previous results [Thai and Thoan, Vietnam J. Math. 2017, doi:10.1007/s10013-017-0259-6].
本文的第一个目的是证明从紧黎曼曲面到复射影空间的全纯映射的第二个主要定理。然后，我们利用它研究了有限总曲率Rm中完全正则极小曲面的广义高斯映射在超曲面上的分支，在次一般位置共享超曲面。结果概括了我们之前的结果[Thai and than, Vietnam J. Math. 2017, doi:10.1007/s10013-017-0259-6]。
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