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<p>We study homeomorphisms that satisfy a Poletsky-type inverse inequality in a domain of the Euclidean space. We prove that the uniform limit of a family of such homeomorphisms is either a homeomorphism into the Euclidean space, or a constant in the extended Euclidean space.</p>

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On convergence of homeomorphisms with inverse modulus inequality

  • 期刊论文

  • 发表日期：

    2025年2月17日

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  • Evgeny Sevost’yanov,
  • Valery Targonskii

摘要

We study homeomorphisms that satisfy a Poletsky-type inverse inequality in a domain of the Euclidean space. We prove that the uniform limit of a family of such homeomorphisms is either a homeomorphism into the Euclidean space, or a constant in the extended Euclidean space.