A Splitting Theorem for Scalar Curvature
A Splitting Theorem for Scalar Curvature
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标量曲率的一个分裂定理
DOI：
10.1002/cpa.21803
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发表时间：
2018-04
影响因子：
3
通讯作者：
Otis Chodosh;M. Eichmair;Vlad Moraru
中科院分区：
文献类型：
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作者：
Otis Chodosh;M. Eichmair;Vlad Moraru
我们证明了一个具有非负数量曲率的黎曼3流形是平坦的，如果它包含一个面积最小化圆柱。这个标量曲率类似于J. Cheeger和D. Gromoll（1971）是由D. Fischer-Colbrie和R. Schoen（1980）和M. Cai和G. Galloway（2000年）。© 2018作者。《纯粹与应用数学通讯》由柯朗数学科学研究所和威利期刊公司出版。
We show that a Riemannian 3‐manifold with nonnegative scalar curvature is flat if it contains an area‐minimizing cylinder. This scalar‐curvature analogue of the classical splitting theorem of J. Cheeger and D. Gromoll (1971) was conjectured by D. Fischer‐Colbrie and R. Schoen (1980) and by M. Cai and G. Galloway (2000). © 2018 the Authors. Communications on Pure and Applied Mathematics is published by the Courant Institute of Mathematical Sciences and Wiley Periodicals, Inc.