{"ID":2893569,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.13189","arxiv_id":"2507.13189","title":"Optimal regularity up to the boundary for Plateau-quasi-minimizers","abstract":"We study the regularity of quasi-minimal sets (in the sense of David and Semmes) with a boundary condition, which can be interpreted as quasi-minimizers of Plateau's problem in co-dimension one. For these Plateau-quasi-minimizers, we establish the optimal regularity, which is a characterization by bi-John domains with Ahlfors regular boundaries. This requires to investigate the Ahlfors regularity and also the uniform rectifiability of those sets, up to the boundary.","short_abstract":"We study the regularity of quasi-minimal sets (in the sense of David and Semmes) with a boundary condition, which can be interpreted as quasi-minimizers of Plateau's problem in co-dimension one. For these Plateau-quasi-minimizers, we establish the optimal regularity, which is a characterization by bi-John domains with...","url_abs":"https://arxiv.org/abs/2507.13189","url_pdf":"https://arxiv.org/pdf/2507.13189v1","authors":"[\"Eve Machefert\"]","published":"2025-07-17T14:58:29Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.AP\"]","methods":"[]","has_code":false}