X. Han

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20232025

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math.GT2025

Nearly geodesic surfaces are filling

Xiaolong Hans Han

Let $M$ be a closed hyperbolic $3$ -manifold. A homotopy class $[S]$ of surfaces in $M$ is filling if any representative cuts $M$ into components contractible in $M$ . We prove that…

math.GT2023

Thurston norms, $L^{2}$ -norms, geodesic laminations, and Lipschitz maps

Xiaolong Hans Han

For closed hyperbolic $3$ -manifolds $M$ with volume less than a constant $V$ , we prove an inequality regarding the geometric $L^{2}$ -norm and the topological Thurston norm, which is…

Nearly geodesic surfaces are filling

Thurston norms, L2-norms, geodesic laminations, and Lipschitz maps

Thurston norms, $L^{2}$ -norms, geodesic laminations, and Lipschitz maps