论文标题
紧凑的方法，即棕色质量的积极性和在平坦和球形环境中具有均值符号边界的歧管的刚度
Compact approach to the positivity of Brown-York mass and rigidity of manifolds with mean-convex boundaries in flat and spherical contexts
论文作者
论文摘要
在本文中，我们取消了什叶派定理的旋转证明，以证明棕色质量的积极性，而无需在欧几里得空间中构建非平滑无限无限平坦的非洲空白，并利用Schoen-Yau和Witten证明的ADM质量的积极性。这种相同的紧凑型方法为平均凸边界的Dirac Operator的第一个非零值特征值提供了最佳的下限\ Cite {hmz}，用于与非负相曲率曲率的紧凑型自旋歧管，这是平均空间中平均值体的刚性结果。据我们所知，相同的机械提供了这种类型的类似但新的结果。
In this article we develope a spinorial proof of the Shi-Tam theorem for the positivity of the Brown-York mass without necessity of building non smooth infinite asymptotically flat hypersurfaces in the Euclidean space and use the positivity of the ADM mass proved by Schoen-Yau and Witten. This same compact approach provides an optimal lower bound \cite{HMZ} for the first non null eigenvalue of the Dirac operator of a mean convex boundary for a compact spin manifold with non negative scalar curvature, an a rigidity result for mean-convex bodies in flat spaces. The same machinery provides analogous, but new, results of this type, as far as we know, in spherical contexts, including a version of Min-Oo's conjecture.
