四维流形中极小曲面最小面积的一个上界
An upper bound for the smallest area of a minimal surface in manifolds of dimension four
摘要：
本文证明了：对于任意具有平凡第一同调群的闭四维黎曼流形$M$，如果里奇曲率$|Ric|\leq3$，直径$diam(M)\leq D$和体积$vol(M)>v>0$，则对于某个只依赖于v和D的函数F，在$M$中的最小二维平稳变倍积分的面积有界于F（v，D）.我们对面积的界是基于对$M$的第一同调填充函数的估计。
英文摘要：
In this paper, we prove that for any closed 4-dimensional Riemannian manifold $M$ with trivial first homology group, if the Ricci curvature $|Ric|\leq3$, the diameter $diam(M)\leq D$ and the volume $vol(M)>v>0$, then the area of a smallest 2-dimensional stationary integral varifold in $M$ is bounded by F(v,D), for some function F that only depends on v and D. Our bound for the area is based on the estimation of the first homological filling function of $M$.
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