The planar Mumford–Shah regularity conjecture and local weak-L^(4) gradient bounds
OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
Resolves the interior regularity conjecture for reduced absolute planar Mumford–Shah minimizers with bounded fidelity data. Locally, the closed discontinuity set is a C^{1,α} arc, a regular crack tip, or three arcs meeting at 120^\circ; only finitely many global connected components meet any compact interior region.
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MANUSCRIPT 01
Interior regularity of planar Mumford–Shah minimizers
We prove the interior regularity assertion of the planar Mumford–Shah conjecture for reduced absolute minimizers with bounded fidelity data. Every interior point of the closed discontinuity set has a neighborhood consisting of a C^{1,α} arc, an arc ending at that point, or three such arcs meeting at 120 degrees. Only finitely…
Full source abstract
We prove the interior regularity assertion of the planar Mumford–Shah conjecture for reduced absolute minimizers with bounded fidelity data. Every interior point of the closed discontinuity set has a neighborhood consisting of a C^{1,α} arc, an arc ending at that point, or three such arcs meeting at 120 degrees. Only finitely many global connected components meet any relatively compact open set.
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