论文标题
晶格中的等量稳定性
Isoperimetric stability in lattices
论文作者
论文摘要
我们在$ \ mathbb {z}^d $上获得了一般cayley digraphs的等速稳定定理。对于任何生成$ \ mathbb {z}^d $在$ \ mathbb {z} $上的固定$ b $，我们表征了$ b $的cayley digraph in of iSoperimetric of $ b $的大致结构，我们必须表明$ a $ a $ a $ a $ a $ a $ kz \ kz \ mathbb^z cap \ capbb { $ z $是$ b $的圆锥形船体，对于边界边界，$ z $是$ b $生成的Zonotope。
We obtain isoperimetric stability theorems for general Cayley digraphs on $\mathbb{Z}^d$. For any fixed $B$ that generates $\mathbb{Z}^d$ over $\mathbb{Z}$, we characterise the approximate structure of large sets $A$ that are approximately isoperimetric in the Cayley digraph of $B$: we show that $A$ must be close to a set of the form $kZ \cap \mathbb{Z}^d$, where for the vertex boundary $Z$ is the conical hull of $B$, and for the edge boundary $Z$ is the zonotope generated by $B$.
