2020/07/29 by Darren King, Francesco Maggi, Salvatore Stuvard
Materials Science · Mathematics · Physics and Astronomy · #Geometry #Gravitational singularity #Limit (mathematics) #Mathematical analysis #Mathematics #Physics #Pickering emulsions and particle stabilization #Plateau (mathematics) #Point processes and geometric inequalities #Pure mathematics #Singularity #Smoothness #Soap film #Stochastic processes and statistical mechanics #Zero (linguistics) #math-ph #math.AP #math.DG #math.MP #msc:49Q20
paper · pdf · doi:10.1007/s00205-021-01727-3
published as Arch. Rational Mech. Anal. Volume 243 no. 2 (2022), pp. 459-500 · 33 pages, 8 figures
arxiv created 2020/07/29 · openalex publication_date 2022/01/06 · arxiv updated 2022/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study generalized minimizers in the soap film capillarity model introduced in [arXiv:1807.05200,arXiv:1907.00551]. Collapsed regions of generalized minimizers are shown to be smooth outside of dimensionally small singular sets, which are thus empty in physical dimensions. Since generalized minimizers converge to Plateau's type surfaces in the vanishing volume limit, the fact that collapsed regions cannot exhibit Y-points and T-points (which are possibly present in the limit Plateau's surfaces) gives the first strong indication that singularities of the limit Plateau's surfaces should always be "wetted" by the bulky regions of the approximating generalized minimizers.