论文标题
无限范围的无穷大的屏障原理具有有限的平均曲率
A barrier principle at infinity for varifolds with bounded mean curvature
论文作者
论文摘要
我们的工作调查了Riemannian歧管中的Varifolds $σ\ subset m $，具有任意的编成和有限的平均曲率，其中包含在一个开放域$ω$中。在对$ m $和$ \ partialω$的曲率的轻度假设下，也允许某些$ \ partialω$的奇异点，我们证明了无限的障碍原理，即，我们表明，$σ$到$ \ \ \ \ \ \ poartialω$的距离是$ \ partial fartial formial fartialitial。我们的定理是Indrienty在varifolds上的最大原则的结果，具有独立的关注。
Our work investigates varifolds $Σ\subset M$ in a Riemannian manifold, with arbitrary codimension and bounded mean curvature, contained in an open domain $Ω$. Under mild assumptions on the curvatures of $M$ and on $\partial Ω$, also allowing for certain singularities of $\partial Ω$, we prove a barrier principle at infinity, namely we show that the distance of $Σ$ to $\partial Ω$ is attained on $\partial Σ$. Our theorem is a consequence of sharp maximum principles at infinity on varifolds, of independent interest.
