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<p>We give conditions for topological and bi-Lipschitz equivalences within a class of mixed singularities of Pham–Brieskorn type. As a consequence, we construct infinite families that are topologically trivial but have distinct bi-Lipschitz types. We also investigate this problem in the context of mixed surfaces defined by these singularities in the case of two complex variables, deriving conditions for inner, outer, and ambient bi-Lipschitz equivalences. In particular, we obtain an invariant of the subanalytic outer geometry of the associated mixed surfaces, which is determined by the exponents.</p>

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Lipschitz geometry of mixed Pham–Brieskorn singularities

  • 期刊论文

  • 发表日期：

    2026年1月14日

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  • Inácio Rabelo

摘要

We give conditions for topological and bi-Lipschitz equivalences within a class of mixed singularities of Pham–Brieskorn type. As a consequence, we construct infinite families that are topologically trivial but have distinct bi-Lipschitz types. We also investigate this problem in the context of mixed surfaces defined by these singularities in the case of two complex variables, deriving conditions for inner, outer, and ambient bi-Lipschitz equivalences. In particular, we obtain an invariant of the subanalytic outer geometry of the associated mixed surfaces, which is determined by the exponents.