论文标题
旋转对称自我收缩术的紧凑性和有限定理
Compactness and finiteness theorems for rotationally symmetric self shrinkers
论文作者
论文摘要
在本说明中，我们首先显示了小于2的熵的旋转对称性自我收缩术的紧凑定理，得出的结论是，在每种$ n \ geq 2 $旋转对称的自我缩水剂中，每个$ n \ geq 2 $都可以最大程度地减少自我收缩的差异为$ s^1 \ s^1 \ times s^{n-1} $。假设额外的对称性，即轮廓曲线是凸，我们删除了熵假设。假设轮廓曲线是反射对称性的，我们表明，只有许多这样的收缩器才能进行刚性运动。
In this note we first show a compactness theorem for rotationally symmetric self shrinkers of entropy less than 2, concluding that there are entropy minimizing self shrinkers diffeomorphic to $S^1 \times S^{n-1}$ for each $n \geq 2$ in the class of rotationally symmetric self shrinkers. Assuming extra symmetry, namely that the profile curve is convex, we remove the entropy assumption. Supposing the profile curve is additionally reflection symmetric we show there are only finitely many such shrinkers up to rigid motion.
