论文标题
$ε$ - 拆分地图的构造
The construction of $ε$-splitting map
论文作者
论文摘要
对于具有非阴性RICCI曲率和几乎最大体积的地理球，我们在不使用紧凑型参数的情况下，我们在均匀的半径均匀半径的同心测地球上构造了$ε$ splatting映射。我们的证明中有两个新的技术要点。第一个是通过感应来查找$ n $定向点的方式，并分层几乎是gu-gu定理。另一个是预测的错误估计，它可以保证我们发现的$ n $定向点确实确定了$ n $不同的方向。
For a geodesic ball with non-negative Ricci curvature and almost maximal volume, without using compactness argument, we construct an $ε$-splitting map on a concentric geodesic ball with uniformly small radius. There are two new technical points in our proof. The first one is the way of finding $n$ directional points by induction and stratified almost Gou-Gu Theorem. The other one is the error estimates of projections, which guarantee the $n$ directional points we find really determine $n$ different directions.
