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A New Intrinsic Metric on Metric Spaces

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Abstract

A new intrinsic metric called \(S_{D}\)-metric is introduced for a general metric space (X, d), where D is a non-trivial bounded closed subset of X. The metric \(S_{D}\) can be used to define a strongly hyperbolic metric on X. We consider the convergence of metric spaces \(\{(X,S_{D_n})\}_{n=1}^{\infty }\) for a sequence of non-trivial bounded closed subsets \(\{D_n\}_{n=1}^{\infty }\). The distortion property of the new metric on the unit ball \(\mathbb {B}^n\) is also studied under the Möbius transformations of the unit ball.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 12071118 and 12026203) and Natural Science Foundation of Hunan Province (Grant No. 2020JJ4163).

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Authors and Affiliations

  1. School of Mathematics, Hunan University, Changsha, 410082, People’s Republic of China

    Yumiao Cui & Yingqing Xiao

  2. Hunan Provincial Key Laboratory of Intelligent Information Processing and Applied Mathematics, Hunan University, Changsha, 410082, China

    Yingqing Xiao

Authors
  1. Yumiao Cui
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  2. Yingqing Xiao
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Correspondence to Yingqing Xiao.

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Communicated by See Keong Lee.

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Cui, Y., Xiao, Y. A New Intrinsic Metric on Metric Spaces. Bull. Malays. Math. Sci. Soc. 45, 2941–2958 (2022). https://doi.org/10.1007/s40840-022-01310-3

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