论文标题
肥皂膜毛细血管模型中塌陷区域的平滑度
Smoothness of collapsed regions in a capillarity model for soap films
论文作者
论文摘要
我们研究了[Arxiv：1807.05200，Arxiv：1907.00551]中引入的肥皂膜毛细血管模型中的广义极小化。广义极小化器的折叠区域被证明是在尺寸小的单数集合外部光滑的，因此在物理尺寸中是空的。由于通用的极小量在消失的体积限制下汇聚到高原的类型表面，因此崩溃的区域不能表现出$ y $ - 点和$ t $ - 点（可能存在于极限高原的表面中），这表明了第一个强烈的迹象表明，极限平原表面的奇异性应始终是“湿润”的奇异范围。
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.
