Scholarlink

<p>For a Kobayashi hyperbolic domain, Abate introduced the notion of small and big horospheres of a given radius at a boundary point with a pole. In this article, we investigate which domains have the property that closed big horospheres and closed small horospheres centered at a given point and of a given radius intersect the boundary only at that point? We prove that any model-Gromov-hyperbolic domain have this property. To provide examples of non-Gromov-hyperbolic domains, we show that unbounded locally model-Gromov-hyperbolic domains and bounded, Dini-smooth, locally convex domains&#xa0;—&#xa0;that are locally visible&#xa0;—&#xa0;also have this property. Finally, using the geometry of the horospheres, we present a result about the homeomorphic extension of biholomorphisms and give an application of it.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Geometry of Horospheres in Kobayashi Hyperbolic Domains

  • 期刊论文

  • 发表日期：

    2025年12月22日

查看全文
  • Vikramjeet Singh Chandel,
  • Nishith Mandal

摘要

For a Kobayashi hyperbolic domain, Abate introduced the notion of small and big horospheres of a given radius at a boundary point with a pole. In this article, we investigate which domains have the property that closed big horospheres and closed small horospheres centered at a given point and of a given radius intersect the boundary only at that point? We prove that any model-Gromov-hyperbolic domain have this property. To provide examples of non-Gromov-hyperbolic domains, we show that unbounded locally model-Gromov-hyperbolic domains and bounded, Dini-smooth, locally convex domains — that are locally visible — also have this property. Finally, using the geometry of the horospheres, we present a result about the homeomorphic extension of biholomorphisms and give an application of it.