Scholarlink

<p>In this paper, we consider the combinatorial <i>p</i>-th Ricci flows in the inversive distance circle packing setting. A primary challenge arises from the fact that the solutions to the flow equations may develop three distinct types of boundary singularities, namely “zero boundary”, “infinity boundary” and “triangle inequality invalid boundary” in finite time due to the inversive distance condition <i>I</i> &gt; 1. Adopting the extension techniques, we establish the long time existence and convergence of the solutions to the combinatorial <i>p</i>-th Ricci flows for inversive distance circle packings in Euclidean (resp., hyperbolic) background geometry. Our results partially generalize the work of Ge and Jiang on the deformation of inversive distance circle packings from <i>p</i> = 2 to any <i>p</i> &gt; 1.</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

Combinatorial p-th Ricci Flows for Inversive Distance Circle Packings

  • 期刊论文

  • 发表日期：

    2026年7月5日

查看全文
  • Longxiang Wu,
  • Rongyuan Liu,
  • Aijin Lin

摘要

In this paper, we consider the combinatorial p-th Ricci flows in the inversive distance circle packing setting. A primary challenge arises from the fact that the solutions to the flow equations may develop three distinct types of boundary singularities, namely “zero boundary”, “infinity boundary” and “triangle inequality invalid boundary” in finite time due to the inversive distance condition I > 1. Adopting the extension techniques, we establish the long time existence and convergence of the solutions to the combinatorial p-th Ricci flows for inversive distance circle packings in Euclidean (resp., hyperbolic) background geometry. Our results partially generalize the work of Ge and Jiang on the deformation of inversive distance circle packings from p = 2 to any p > 1.