山东理工大学学报（自然科学版）2026，Vol.40Issue(3)：67-71,5.
基于边界调控的双曲型度量构造及其几何分析
Construction and geometric analysis of a hyperbolic-type metric based on boundary control
黎纪啸 1张孝惠1
作者信息
- 1. 浙江理工大学 理学院,浙江 杭州 310018
- 折叠
摘要
Abstract
This article proposes a boundary-controlled hyperbolic-type metric to address the limitations of classical hyperbolic metric in high-dimensional and general metric spaces.By introducing a boundary dis-tance adjustment factor,a clear definition and construction method for the new metric are provided,and its positive definiteness,symmetry,the triangle inequality,and completeness are proved.This study shows that under this metric,identity mappings exhibit quasi-conformality,and the metric balls in the upper half space and the unit ball are convex.关键词
度量空间/双曲型度量/拟共形性/增长性Key words
metric space/hyperbolic-type metric/quasi-conformality/growth分类
数理科学引用本文复制引用
黎纪啸,张孝惠..基于边界调控的双曲型度量构造及其几何分析[J].山东理工大学学报（自然科学版）,2026,40(3):67-71,5.
