论文标题
稳定的condimension的结构一个积分varifolds附近的密度$ q+1/2 $附近的结构
The Structure of Stable Codimension One Integral Varifolds near Classical Cones of Density $Q+1/2$
论文作者
论文摘要
对于每个积极整数$ q \ in \ mathbb {z} _ {\ geq 2} $，我们证明了一个多价值的$ c^{1，α} $ varifolds for varifolds for类$ \ mathcal $ \ mathcal {s}}}} _q $，即顶点密度$ <q $，足够接近固定的积分锥，由$ 2Q+1 $ 1 $ half hyperplanes（以多重性计数）组成。这样的结果进一步发展了对本地结构的理解（可能是分支）varifolds中的$ \ Mathcal {s} _q $是由作者和N.〜Wickramasekera（\ cite {minterwick}）实现的\ Mathbb {z} _ {\ geq 2} $。与以前的作品的一个显着区别是，我们的方法不需要对设置（密度$ q $）分支的任何先验尺寸限制来排除密度间隙。
For each positive integer $Q\in\mathbb{Z}_{\geq 2}$, we prove a multi-valued $C^{1,α}$ regularity theorem for varifolds in the class $\mathcal{S}_Q$, i.e., stable codimension one stationary integral $n$-varifolds which have no classical singularities of vertex density $<Q$, which are sufficiently close to a stationary integral cone comprised of $2Q+1$ half-hyperplanes (counted with multiplicity) meeting along a common axis. Such a result furthers the understanding of the local structure about singularities in the (possibly branched) varifolds in $\mathcal{S}_Q$ achieved by the author and N.~Wickramasekera (\cite{minterwick}) and generalises the authors' previous work in the case $Q=2$ (\cite{minter-5-2}) to arbitrary $Q\in \mathbb{Z}_{\geq 2}$. One notable difference with previous works is that our methods do not need any a priori size restriction on the (density $Q$) branch set to rule out density gaps.
