{"title":"在赫尔维茨度规上","authors":"Amar Deep Sarkar, Kaushal Verma","doi":"10.2996/KMJ44108","DOIUrl":null,"url":null,"abstract":"The Hurwitz metric was recently defined by Minda by considering a variational problem that involves holomorphic maps from the disc that are globally injective at the origin. In this note, sharp boundary estimates for this metric are obtained on $C^2$-smooth planar domains and as a consequence, it is shown that it is uniformly comparable with the Caratheodory and Kobayashi metrics on such domains. In addition, estimates for the generalized curvatures of this metric are also given.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Hurwitz metric\",\"authors\":\"Amar Deep Sarkar, Kaushal Verma\",\"doi\":\"10.2996/KMJ44108\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Hurwitz metric was recently defined by Minda by considering a variational problem that involves holomorphic maps from the disc that are globally injective at the origin. In this note, sharp boundary estimates for this metric are obtained on $C^2$-smooth planar domains and as a consequence, it is shown that it is uniformly comparable with the Caratheodory and Kobayashi metrics on such domains. In addition, estimates for the generalized curvatures of this metric are also given.\",\"PeriodicalId\":54747,\"journal\":{\"name\":\"Kodai Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Kodai Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2996/KMJ44108\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kodai Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2996/KMJ44108","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
The Hurwitz metric was recently defined by Minda by considering a variational problem that involves holomorphic maps from the disc that are globally injective at the origin. In this note, sharp boundary estimates for this metric are obtained on $C^2$-smooth planar domains and as a consequence, it is shown that it is uniformly comparable with the Caratheodory and Kobayashi metrics on such domains. In addition, estimates for the generalized curvatures of this metric are also given.
期刊介绍：
Kodai Mathematical Journal is edited by the Department of Mathematics, Tokyo Institute of Technology. The journal was issued from 1949 until 1977 as Kodai Mathematical Seminar Reports, and was renewed in 1978 under the present name. The journal is published three times yearly and includes original papers in mathematics.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
