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<p>The contribution of this paper is to provide some necessary and sufficient conditions for quasihyperbolic geodesics in a proper subdomain of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^n\)</EquationSource> </InlineEquation> to be diameter double cone arcs with the parameter independent of <i>n</i>. As a result, we provide an alternative proof of the following statement: quasihyperbolic geodesics in a proper domain in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {R}^n\)</EquationSource> </InlineEquation> are double cone curves if and only if it is LLC<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(_2\)</EquationSource> </InlineEquation> and has the ball separation property, which is a special case of a recent result of Guo-Huang-Wang.</p>

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The double cone property for quasihyperbolic geodesics

  • 期刊论文

  • 发表日期：

    2026年4月28日

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  • Qingshan Zhou,
  • Zhoucheng Zheng,
  • Xining Li,
  • Liulan Li

摘要

The contribution of this paper is to provide some necessary and sufficient conditions for quasihyperbolic geodesics in a proper subdomain of \(\mathbb {R}^n\) to be diameter double cone arcs with the parameter independent of n. As a result, we provide an alternative proof of the following statement: quasihyperbolic geodesics in a proper domain in \(\mathbb {R}^n\) are double cone curves if and only if it is LLC \(_2\) and has the ball separation property, which is a special case of a recent result of Guo-Huang-Wang.