发表机构
University of Science and Technology of China（中国科学技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明正第一牛顿变换的闭余定向超曲面浸入可填充为紧致浸入流形，并由此结合刚性结果推出常数量曲率浸入超曲面必为球面。
AI 中文摘要
我们证明，在$\R^{n+1}$（$n\ge 2$）中，每个闭的、余定向的超曲面浸入，若其第一牛顿变换正定，则它界定了一个紧致浸入流形，且具有给定的边界映射和向外余定向。结合Ros和Pinkall的刚性结果，此填充定理蕴含：$\R^{n+1}$中每个闭连通且具有常数量曲率的浸入超曲面都是标准球面。
英文摘要
We prove that every closed cooriented hypersurface immersion in $\R^{n+1}$, $n\ge 2$, with positive definite first Newton transformation bounds a compact immersed manifold with the prescribed boundary map and outward coorientation. Combined with the rigidity results of Ros and Pinkall, this filling theorem implies that every closed connected hypersurface immersed in $\R^{n+1}$ with constant scalar curvature is a round sphere.
Comments20 pages
