{"title":"庞加莱公设与伯格曼理论","authors":"Steven G. Krantz","doi":"10.1137/22m1544622","DOIUrl":null,"url":null,"abstract":"SIAM Review, Volume 66, Issue 2, Page 355-367, May 2024. <br/> We treat the Poincaré metric on the disc. In particular we emphasize the fact that it is the canonical holomorphically invariant metric on the unit disc. Then we generalize these ideas to the Bergman metric on a domain in complex space. Along the way we treat the Bergman kernel and study its invariance and uniqueness properties.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":"30 1","pages":""},"PeriodicalIF":10.8000,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Poincaré Metric and the Bergman Theory\",\"authors\":\"Steven G. Krantz\",\"doi\":\"10.1137/22m1544622\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Review, Volume 66, Issue 2, Page 355-367, May 2024. <br/> We treat the Poincaré metric on the disc. In particular we emphasize the fact that it is the canonical holomorphically invariant metric on the unit disc. Then we generalize these ideas to the Bergman metric on a domain in complex space. Along the way we treat the Bergman kernel and study its invariance and uniqueness properties.\",\"PeriodicalId\":49525,\"journal\":{\"name\":\"SIAM Review\",\"volume\":\"30 1\",\"pages\":\"\"},\"PeriodicalIF\":10.8000,\"publicationDate\":\"2024-05-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Review\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/22m1544622\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Review","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/22m1544622","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
SIAM Review, Volume 66, Issue 2, Page 355-367, May 2024. We treat the Poincaré metric on the disc. In particular we emphasize the fact that it is the canonical holomorphically invariant metric on the unit disc. Then we generalize these ideas to the Bergman metric on a domain in complex space. Along the way we treat the Bergman kernel and study its invariance and uniqueness properties.
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Survey and Review feature papers that provide an integrative and current viewpoint on important topics in applied or computational mathematics and scientific computing. These papers aim to offer a comprehensive perspective on the subject matter.
Research Spotlights publish concise research papers in applied and computational mathematics that are of interest to a wide range of readers in SIAM Review. The papers in this section present innovative ideas that are clearly explained and motivated. They stand out from regular publications in specific SIAM journals due to their accessibility and potential for widespread and long-lasting influence.
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