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<p>In this paper, we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane. This estimate involves a relationship between the Hausdorff distance to a geodesic ball and the deficit in the isoperimetric inequality, where the coefficient of the deficit is a universal constant.</p>

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Stability of the isoperimetric inequality in hyperbolic plane

  • 期刊论文

  • 发表日期：

    2025年1月24日

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  • Haizhong Li,
  • Yao Wan

摘要

In this paper, we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane. This estimate involves a relationship between the Hausdorff distance to a geodesic ball and the deficit in the isoperimetric inequality, where the coefficient of the deficit is a universal constant.