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The closedness conjecture for maximal FL zones

Let WW be a wedge for the graph 4z=f(x,y)44z=f(x,y)4, and let an FLFL zone be a region classified as FLFL according to the preceding definitions. A maximal FLFL zone is an FLFL zone not properly contained in any other FLFL zone.

Closedness conjecture. Maximal FLFL zones are closed.

This concerns the structure of the zones determined by the geometry of the real surface singularity and its tangent cone. The supplied text does not state whether the conjecture has been proved or disproved, so its status remains open.

Sources & referencesView supporting material

Primary source

Donal O'Shea and Leslie Wilson, “Bilipschitz geometry of real surface singularities whose tangent cone is a plane”, arXiv:2408.07218 (2025).

bilipschitz-geometryreal-surface-singularities

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