Xiangsen Qin

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20242026

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math.DG2026

Chern Holomorphic Sectional Curvature: Canonical Ampleness, Rigidity, and Flatness Counterexamples

Xiangsen Qin, Yuanhong Tian

Let $X$ be a compact Brody-hyperbolic complex manifold admitting a strictly positive real $(1, 1)$ -current $T$ with smooth $d T$ and $d d^{c} T \leq 0$ . We prove that the canonical bundle $…

math.DG2025

$L^{2}$ -estimates on flat vector bundles and Prékopa's theorem

Gang Huang, Weiwen Jiang, Xiangsen Qin

In this paper, we will construct Hörmander's $L^{2}$ -estimate of the operator $d$ on a flat vector bundle over a $p$ -convex Riemannian manifold and discuss some geometric application…

Chern Holomorphic Sectional Curvature: Canonical Ampleness, Rigidity, and Flatness Counterexamples

L2-estimates on flat vector bundles and Prékopa's theorem

$L^{2}$ -estimates on flat vector bundles and Prékopa's theorem