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<p>We construct symmetric self-similar Dirichlet forms that satisfy sub-Gaussian heat kernel estimates on two types of polygon carpets, which are natural generalizations of planner Sierpinski carpets (SC). The first ones are called perfect polygon carpets that are natural analogs of SC in that any intersection cells are either side-to-side or point-to-point. The second ones are called bordered polygon carpets which satisfy the boundary including condition as SC but allow distinct contraction ratios.</p>

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Self-similar Dirichlet forms on polygon carpets

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Shiping Cao,
  • Hua Qiu,
  • Yizhou Wang

摘要

We construct symmetric self-similar Dirichlet forms that satisfy sub-Gaussian heat kernel estimates on two types of polygon carpets, which are natural generalizations of planner Sierpinski carpets (SC). The first ones are called perfect polygon carpets that are natural analogs of SC in that any intersection cells are either side-to-side or point-to-point. The second ones are called bordered polygon carpets which satisfy the boundary including condition as SC but allow distinct contraction ratios.