The Poincaré Metric and the Bergman Theory

IF 10.8 1区数学 Q1 MATHEMATICS, APPLIED

SIAM Review Pub Date : 2024-05-09 DOI:10.1137/22m1544622

Steven G. Krantz

引用次数: 0

Abstract

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.

查看原文本刊更多论文

庞加莱公设与伯格曼理论

SIAM 评论》，第 66 卷，第 2 期，第 355-367 页，2024 年 5 月。我们讨论了圆盘上的庞加莱度量。我们特别强调了它是单位圆盘上的典型全形不变度量这一事实。然后，我们将这些观点推广到复数空间域上的伯格曼度量。在此过程中，我们将处理伯格曼核，并研究其不变性和唯一性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

SIAM Review 数学-应用数学

CiteScore

16.90

自引率

0.00%

发文量

期刊介绍： 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.