论文标题
平均凸正确嵌入$ [φ，\ vec {e} _ {3}] $ - $ \ mathbb {r}^3 $中的最小表面
Mean convex properly embedded $[φ,\vec{e}_{3}]$-minimal surfaces in $\mathbb{R}^3$
论文作者
论文摘要
我们建立了平均凸的曲率估计值和凸度结果，正确嵌入$ [φ，\ vec {e} _ {3}] $ - 在$ \ mathbb {r}^3 $，即$ -minimal coreface y时仅$ coortions $ coordation $ coordation $ {$ coortions $ { Led by the works on curvature estimates for surfaces in 3-manifolds, due to White for minimal surfaces, to Rosenberg, Souam and Toubiana, for stable CMC surfaces, and to Spruck and Xiao for stable translating solitons in $\mathbb{R}^3$, we use a compactness argument to provide curvature estimates for a family of mean convex $ [φ，\ vec {e} _ {3}] $ - $ \ mathbb {r}^{3} $中的最小表面。我们将此结果应用于概括spruck和xiao的凸属性，以翻译孤子。更准确地说，我们表征了正确嵌入的$ [φ，\ vec {e} _ {3}] $ - 在$ \ mathbb {r}^{3} $中的最小表面，而无正平均曲率是无效的，而无正值的曲率是$φ$的生长，而$φ$的生长最多。
We establish curvature estimates and a convexity result for mean convex properly embedded $[φ,\vec{e}_{3}]$-minimal surfaces in $\mathbb{R}^3$, i.e., $φ$-minimal surfaces when $φ$ depends only on the third coordinate of $\mathbb{R}^3$. Led by the works on curvature estimates for surfaces in 3-manifolds, due to White for minimal surfaces, to Rosenberg, Souam and Toubiana, for stable CMC surfaces, and to Spruck and Xiao for stable translating solitons in $\mathbb{R}^3$, we use a compactness argument to provide curvature estimates for a family of mean convex $[φ,\vec{e}_{3}]$-minimal surfaces in $\mathbb{R}^{3}$. We apply this result to generalize the convexity property of Spruck and Xiao for translating solitons. More precisely, we characterize the convexity of a properly embedded $[φ,\vec{e}_{3}]$-minimal surface in $\mathbb{R}^{3}$ with non positive mean curvature when the growth at infinity of $φ$ is at most quadratic.
