论文标题
带有旋转对称性的嵌入式自我撕裂器的熵边界，紧凑性和有限定理
Entropy Bounds, Compactness and Finiteness Theorems for Embedded Self-shrinkers with Rotational Symmetry
论文作者
论文摘要
在这项工作中，我们研究了$ \ mathbb {r}^{n+1} $中完整嵌入式旋转自身自身缩短的超曲面的空间。首先，使用比较几何形状在度量几何形状的上下文中，我们为所有这些自我脱落器的熵提供了明确的上限。其次，作为应用程序，我们证明了所有此类收缩器空间上的平滑紧凑定理。我们还证明，只有许多这样的自碎者和额外的反射对称性有限。
In this work, we study the space of complete embedded rotationally symmetric self-shrinking hypersurfaces in $\mathbb{R}^{n+1}$. First, using comparison geometry in the context of metric geometry, we derive explicit upper bounds for the entropy of all such self-shrinkers. Second, as an application we prove a smooth compactness theorem on the space of all such shrinkers. We also prove that there are only finitely many such self-shrinkers with an extra reflection symmetry.
