{"id":"openai-math/Interior-regularity-of-planar-Mumford-Shah-minimizers","pdf":"https://github.com/openai/math/blob/main/preprints/Interior-regularity-of-planar-Mumford-Shah-minimizers-September-24-2026/Interior-regularity-of-planar-Mumford-Shah-minimizers-September-24-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/Interior-regularity-of-planar-Mumford-Shah-minimizers-September-24-2026","tags":["calculus-of-variations","image-segmentation","geometric-measure-theory"],"score":0,"title":"Interior regularity of planar Mumford–Shah minimizers","domain":"Partial differential equations","family":"366","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AP","summary":"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 $`C^{1,\\alpha}`$ 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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"The planar Mumford–Shah regularity conjecture and local weak- L 4 gradient bounds"}