论文标题
在ricci曲率上的加藤界限下的圆环稳定性
Torus stability under Kato bounds on the Ricci curvature
论文作者
论文摘要
对于封闭的riemannian歧管，我们显示了两个稳定性结果，其RICCI曲率在Kato的意义上很小，其第一个Betti数量等于尺寸。第一个是几何稳定性结果，表明这种歧管是Gromov-Hausdorff靠近平坦的圆环。第二个指出，在更强的假设下，这种歧管对圆环是差异的：这扩展了通过在RICCI曲率下的下限的背景下获得的冷和脸颊冷的结果。
We show two stability results for a closed Riemannian manifold whose Ricci curvature is small in the Kato sense and whose first Betti number is equal to the dimension. The first one is a geometric stability result stating that such a manifold is Gromov-Hausdorff close to a flat torus. The second one states that, under a stronger assumption, such a manifold is diffeomorphic to a torus: this extends a result by Colding and Cheeger-Colding obtained in the context of a lower bound on the Ricci curvature.
