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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
Jingche Chen, Han Hong, Haizhong Li
In this paper, we prove that complete noncompact constant mean curvature hypersurfaces in with finite index must be minimal. This provides a positive answer to do Ca…