Local Lipschitz geometry of weighted homogeneous surfaces

TL;DR

This paper computes the complete bi-Lipschitz invariants, called Hoelder Complexes, for germs of real weighted homogeneous algebraic or semialgebraic surfaces, advancing understanding of their geometric classification.

Contribution

It introduces the computation of Hoelder Complexes as bi-Lipschitz invariants specifically for weighted homogeneous surfaces, providing a new tool for their geometric analysis.

Findings

Hoelder Complexes are complete bi-Lipschitz invariants for these surfaces

Explicit computation methods for these invariants are developed

Results facilitate classification of weighted homogeneous surface germs

Abstract

We compute Hoelder Complexes,i.e. the complete bi-Lipschitz invariants, for germs of real weighed homogeneous algebraic or semialgebraic surfaces.