Lipschitz Geometry of Mixed Pham-Brieskorn Singularities

Abstract

We give conditions for topological and bi-Lipschitz equivalences within a class of mixed singularities of Pham-Brieskorn type. We then derive the construction of topologically trivial infinite families with distinct bi-Lipschitz types. We also investigate the same problem applied to the mixed surfaces defined by these singularities in the two complex variables case and deduce conditions for inner, outer, and ambient bi-Lipschitz equivalences.

Figures (2)

• Figure 1: Mixed surfaces and the respective tangent cones for $a_{1} = 0$
• Figure 2: Projection of $\lambda(s)$ on $\mathbb{C}^{*}$

Theorems & Definitions (50)

• Theorem 2.1: Section 4, sara - Corollary, trot
• Definition 2.2: Definition 2.1, sam
• Lemma 2.3: vico, Lemma 2.3
• Proposition 2.4: Remark 2.2, vico
• Remark 2.5
• Theorem 2.6: Theorem 3.2, sam
• Definition 2.7
• Theorem 2.8
• Theorem 2.9: Theorem 4.1, levwei
• Definition 2.10