论文标题
$ \ mathbf {r}^{4} $中的稳定各向异性最小超曲面
Stable anisotropic minimal hypersurfaces in $\mathbf{R}^{4}$
论文作者
论文摘要
我们表明，在$ \ mathbf {r}^4 $中，完整的，双面稳定的各向异性最小的高表皮具有内在的立方量增长，只要参数椭圆形成$ c^2 $ -Close to to该区域功能。我们还获得了单位球中稳定各向异性最小曲面的内部体积上限。我们可以在所有结果中明确估算常数。 特别是，本文提供了我们最近稳定的伯恩斯坦定理的替代证明，用于$ \ mathbf {r}^4 $中的最小性超曲面。新的证明与严格阳性标态曲率的研究的技术密切相关。
We show that a complete, two-sided, stable immersed anisotropic minimal hypersurface in $\mathbf{R}^4$ has intrinsic cubic volume growth, provided the parametric elliptic integral is $C^2$-close to the area functional. We also obtain an interior volume upper bound for stable anisotropic minimal hypersurfaces in the unit ball. We can estimate the constants explicitly in all of our results. In particular, this paper gives an alternative proof of our recent stable Bernstein theorem for minimal hypersurfaces in $\mathbf{R}^4$. The new proof is more closely related to techniques from the study of strictly positive scalar curvature.
