Concentration of curvature and Lipschitz invariants of holomorphic functions of two variables

Abstract

By combining analytic and geometric viewpoints on the concentration of the curvature of the Milnor fibre, we prove that Lipschitz homeomorphisms preserve the zones of multi-scale curvature concentration as well as the gradient canyon structure of holomorphic functions of two variables. This yields the first new Lipschitz invariants after those discovered by Henry and Parusinski in 2003.

25 pages, small corrections; last version before publication

References in corpus (3)

• The thick-thin decomposition and the bilipschitz classification of normal surface singularities
• Lipschitz geometry of complex surfaces: analytic invariants and equisingularity
• A'Campo curvature bumps and the Dirac phenomenon near a singular point

Cited by in corpus (1)

• Clustering polar curves