AI 中文总结
该研究针对闭凯勒曲面证实了格罗莫夫定量数量曲率-单纯体积猜想的核心估计，还构造了无穷多满足相同估计的一般类型非凯勒辛4流形，推进了相关几何猜想的验证与拓展。
AI 中文摘要
设M为闭凯勒曲面，我们证明M上满足数量曲率Sc_g≥-λ²（λ≥0）的任一黎曼度量g，均满足∥M∥≤(27/2)λ⁴ vol_g(M)，这证实了闭凯勒曲面的格罗莫夫定量数量曲率-单纯体积猜想。我们还构造了无穷多个具有正单纯体积的一般类型非凯勒辛4流形，且上述估计对其成立。
英文摘要
Let $M$ be a closed Kähler surface. We prove that every Riemannian metric $g$ on $M$ with $\operatorname{Sc}_g\geq-λ^2$, where $λ\geq 0$, satisfies $$ \lVert M\rVert\leq \frac{27}{2}\,λ^4\operatorname{vol}_g(M). $$ This proves Gromov's quantitative scalar-curvature--simplicial-volume conjecture for closed Kähler surfaces. We also construct infinitely many non-Kähler symplectic 4-manifolds of general type with positive simplicial volume for which the same estimate holds.
Comments23 pages. Comments are welcome!
