论文标题
Willmore表面和应用的无微量曲率的能量估计
Energy Estimates for the Tracefree Curvature of Willmore Surfaces and Applications
论文作者
论文摘要
我们证明了$ε$ -REGUMENTITY结果，对于带有界面的第二个基本形式的Willmore表面的痕迹曲率。对于这样的表面，我们研究了对其$ l^2 $ -norm的少量控制。值得注意的是，我们得出了上述类型表面的差距。我们进一步运用结果来推断出常规性结果，以最小的间距浸入de sitter空间$ s^{4,1} $。
We prove an $ε$-regularity result for the tracefree curvature of a Willmore surface with bounded second fundamental form. For such a surface, we obtain a pointwise control of the tracefree second fundamental form from a small control of its $L^2$-norm.Several applications are investigated. Notably, we derive a gap statement for surfaces of the aforementioned type. We further apply our results to deduce regularity results for conformal minimal spacelike immersions into the de Sitter space $S^{4,1}$.
