Time：9:00-10:00, Tuesday, January 20 2026
Venue：E14-212
Host：Jintian Zhu, ITS
Speaker：Zhengnan Chen, Peking University
Title：Manifolds with positive isotropic curvature in higher dimensions
Language: Chinese
Abstract：Positive isotropic curvature (PIC for short) was introduced by Micallef-Moore and is a natural curvature condition that makes sense in dimension n≥4. It has been conjectured that every compact n-dimensional PIC manifold must be diffeomorphic to a connected sum of finitely many spaces, each of which is a metric quotient of S^n or S^{n-1}×R. By a work of Simon Brendle in 2019, the conjecture is true with additional assumptions that the manifold has dimension at least 12 and contains no nontrivial incompressible (n-1)-dimensional space forms. The dimension restriction is due to his pinching estimate. In our recent work, we improved this pinching estimate and showed that the dimension restriction can be loosed to at least 9. We expect to obtain suitable pinching estimate for the missing dimensions 5≤n≤8 in the future.
