From the 1 of 10 linked papers with an AI index.
10 papers
Curvature-free effects from volume growth and ends-counting and their applications
Yuchen Bi, Jintian Zhu
The paper proves that manifolds with certain volume growth or many ends have special geometric structures, and uses these results to give new proofs of known theorems without relyi…
Positive Scalar Curvature Obstructions via Singular Dimension Descent
Yuchen Bi, Jintian Zhu
In light of recent advances in conformal blow-up methods for the positive mass theorem, including He--Shi--Yu, Bi--Hao--He--Shi--Zhu, and Brendle--Wang, we develop a Schoen--Yau ty…
Riemannian Penrose inequality in all dimensions
Yuchen Bi, Jintian Zhu
We prove the Riemannian Penrose inequality in arbitrary dimension for smooth complete asymptotically flat manifolds with nonnegative scalar curvature and compact outer-minimizing m…
A proof for the Riemannian positive mass theorem up to dimension 19
Yuchen Bi, Tianze Hao, Shihang He +2
In this paper, we prove the Riemannian positive mass theorem up to dimension , building on a combination of torical symmetrization and the singularity blow-up technique develop…
Interior control for surfaces with positive scalar curvature and its application
Shuli Chen, Jianchun Chu, Jintian Zhu
Let , , be a closed aspherical -manifold and a subset consisting of disjoint incompressible embedded closed aspherical submanifolds (possibly…
Positive scalar curvature metrics and aspherical summands
Shuli Chen, Jianchun Chu, Jintian Zhu
We prove for that the connected sum of a closed aspherical -manifold with an arbitrary non-compact manifold does not admit a complete metric with nonnegative sca…