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arXiv · 2608.17335

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

Jie Min·Fangyang Zheng·Bo Zhu
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Abstract

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 closed K\"ahler surfaces. We also construct infinitely many non-K\"ahler symplectic 4-manifolds of general type with positive simplicial volume for which the same estimate holds.

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Jie Min, Fangyang Zheng, Bo Zhu. 2026-08-18. Simplicial Volume and Scalar Curvature on Closed K\"ahler Surfaces. https://arxiv.org/abs/2608.17335

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