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Structure of Torus Fibration Under the First Betti Number Restriction
Xin Peng, Bing Wang, Zhenjian Wang
We study torus bundles with affine structure groups. First, we establish a rigidity result under constraints on the first Betti numbers: If $ \text{b}_{1}(M)-\text{b}_{1}(N)=\dim M…
Two Comments on "Laplace comparison on Kahler Ricci flow and convergence (arXiv:2509.14820v1)"
Xiuxiong Chen, Bing Wang
We clarify the definition of polarized canonical radius in the study of Kahler Ricci flow.
Curvature at the infinity of asymptotically flat Einstein manifold
Bing Wang, Hao Yin
In this paper, we construct coordinates at the infinity of an asymptotically flat end of a Ricci-flat manifold as long as the norm of the curvature is finite i…
Canonical diffeomorphisms of manifolds near spheres
Bing Wang, Xinrui Zhao
For a given Riemannian manifold which is near standard sphere in the Gromov-Hausdorff topology and satisfies , it is known by Cheeger-Col…
Ricci curvature integrals, local functionals, and the Ricci flow
Yuanqing Ma, Bing Wang
Consider a Riemannian manifold whose volume is the same as the standard sphere . If and $\int_{M} \left\{ Rc-(m-1)g\right\}_{-}^{p}…
Rigidity of the round cylinders in Ricci shrinkers
Yu Li, Bing Wang
In this paper, we prove that the round cylinders are rigid in the space of Ricci shrinkers. Namely, any Ricci shrinker that is sufficiently close to in th…