Demonstrates a complete classification of inner Lipschitz geometry in complex surfaces with non-isolated singularities, indicating its broader implications.
Let $(X,0)$ be a germ of a reduced and irreducible complex surface embedded in (Cᵏ,0). In this paper, we give a complete invariant of the inner Lipschitz geometry of complex surface germs, extending the result of Birbrair--Neumann--Pichon {BNP} to the non-isolated case. This invariant is expressed in terms of numerical invariants associated with the coordinate functions f₁,,fₖ of the normalization map n:(X̄,0)→ (X,0)⊂(Cᵏ,0), together with the combinatorics of a suitable good resolution of (X̄,0).
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Yenni Cherik (2026) studied this question.
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