Author

Xiao-Dong Wang

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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 Sep 2026

Spectral Improvements of Geometric Inequalities on Closed K\"ahler Manifolds

Let $(M,g,J)$ be a closed K\"ahler manifold satisfying $\operatorname{Ric}\geqslant g$. We establish improved Liouville theorems for the Euler--Lagrange equations associated with the Beckner--Sobolev inequalities by incorporating the first positive eigenvalue of the $\bar\partial$-Laplacian into a differential-identity...

Sayan Chakraborty, Xiao-Dong Wang, Tian Wu · 0 citations