Author

Bo Zhu

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Preprint Oct 2026

Volume Entropy and Scalar Curvature near a Hyperbolic Metric

Let $(M^n,g_0)$ be a closed hyperbolic manifold, $n\geq3$. We compute the Hessian of volume entropy at $g_0$ under the constraint $Sc_g=-n(n-1)$ and express it as a quadratic form on transverse-traceless symmetric two-tensors. In dimension three, the Hessian is negative definite, and every sufficiently $C^\infty$-close...

Xiao-Dong Wang, Bo Zhu · 0 citations

Preprint Aug 2026

Simplicial Volume and Scalar Curvature on Closed K\"ahler Surfaces

Let $M$ be a closed K\"ahler surface. We prove that every Riemannian metric $g$ on $M$ with $\operatorname{Sc}_g\geq-\lambda^2$, where $\lambda\geq 0$, satisfies $$ \lVert M\rVert\leq \frac{27}{2}\,\lambda^4\operatorname{vol}_g(M). $$ This proves Gromov's quantitative scalar-curvature--simplicial-volume conjecture for...

Jie Min, Fang-Yang Zheng, Bo Zhu · 0 citations