Jingche Chen

collaborators

3 papers

math.DG2026

Intermediate curvature and splitting theorem

Jingche Chen, Han Hong

In this paper, we prove several rigidity results for complete noncompact manifolds with nonnegative intermediate curvatures. We show that when either $3 \leq n \leq 5$ , $1\leq m\leq…

math.DG2025

Nonexistence of the metric with positive intermediate curvatures on manifolds with boundary

Jingche Chen, Han Hong

We establish curvature obstruction theorems for manifolds with boundary. Our main theorems show that, for dimensions up to 7, a topologically nontrivial compact manifold with bound…

math.DG2025

Do Carmo's problem for CMC hypersurfaces in $R^{6}$

Jingche Chen, Han Hong, Haizhong Li

In this paper, we prove that complete noncompact constant mean curvature hypersurfaces in $R^{6}$ with finite index must be minimal. This provides a positive answer to do Ca…

Intermediate curvature and splitting theorem

Nonexistence of the metric with positive intermediate curvatures on manifolds with boundary

Do Carmo's problem for CMC hypersurfaces in R6

Do Carmo's problem for CMC hypersurfaces in $R^{6}$