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Volume Entropy and Scalar Curvature near a Hyperbolic Metric
Xiaodong Wang, Bo Zhu
Let be a closed hyperbolic manifold, . We compute the Hessian of volume entropy at under the constraint and express it as a quadratic form…
Cheeger constant rigidity for cocompact negatively curved manifolds
Kuntao Jin, Xiaodong Wang, Bo Zhu
Let , , be a closed connected Riemannian manifold with $\secg_g\leq-1$, and let be its universal cover. Yau proved that $\hiso(X)\geq m-1$. We prove that…
Simplicial Volume and Scalar Curvature on Closed Kähler Surfaces
Jie Min, Fangyang Zheng, Bo Zhu
Let be a closed Kähler surface. We prove that every Riemannian metric on with , where , satisfies $$ \lVert M\rVert\leq \frac{27}{…
McKean Rigidity for Cocompact Negatively Curved Manifolds and the \(p\)-Laplacian
Kuntao Jin, Bo Zhu
Let \((M^m,g)\) be a closed Riemannian manifold with \(\sec_g\leq-1\). We prove that the bottom spectrum of its universal cover attains McKean's lower bound if and only if the univ…
Scalar curvature, sharp bottom spectrum and geometric rigidity
Jinmin Wang, Bo Zhu
We prove rigidity in the equality case of the sharp bottom spectrum estimate under scalar curvature lower bound. Under the same topological assumptions as in our previous work, a c…
Gromov's Simplicial Volume Vanishing Conjecture for Positive Scalar Curvature
Qiaochu Ma, Jinmin Wang, Zhizhang Xie +2
In this paper, we prove Gromov's simplicial volume vanishing conjecture for closed manifolds with spin universal cover. More precisely, we show that if a closed oriented manifold a…
Bounding the A-hat genus using scalar curvature lower bounds and isoperimetric constants
Qiaochu Ma, Jinmin Wang, Guoliang Yu +1
In this paper, we prove an upper bound on the genus of a smooth, closed, spin Riemannian manifold using its scalar curvature lower bound, Neumann isoperimetric consta…
Scalar-mean rigidity theorem for compact manifolds with boundary
Jinmin Wang, Zhichao Wang, Bo Zhu
We prove a scalar-mean rigidity theorem for compact Riemannian manifolds with boundary in dimension less than five by developing a dimension reduction argument for mean curvature,…
Sharp bottom spectrum and scalar curvature rigidity
Jinmin Wang, Bo Zhu
We establish a sharp upper bound for the bottom spectrum of the Beltrami Laplacian on universal covers of closed Riemannian manifolds with a scalar curvature lower bound. Moreover,…
Scalar curvature rigidity of the four-dimensional sphere
Simone Cecchini, Jinmin Wang, Zhizhang Xie +1
Let be a closed connected oriented (possibly non-spin) smooth four-dimensional manifold with scalar curvature bounded below by . In this paper, we prove that if …
Filling Radius, Quantitative -theory and Positive Scalar Curvature
Jinmin Wang, Zhizhang Xie, Guoliang Yu +1
We prove a quantitative upper bound on the filling radius of complete, spin manifolds with uniformly positive scalar curvature using the quantitative operator -theory and index…