论文标题
等距浸入的Weyl问题重新审视
The Weyl problem of isometric immersions revisited
论文作者
论文摘要
由于Weyl及其概括，我们将$ \ Mathbb {S}^2 $的等距沉浸液重新审视了经典问题，并简单地连接了$ 3 $ 3 $二维的Riemannian歧管，具有非校长高斯曲率。对于存在全局$ c^{1,1} $ - 等距沉浸液的存在，有足够的条件。我们的发展是基于Labourie的框架（浸入IsométriquesElliptiques et courbes pseudo-Holomorphes，J。Diff。Geom。30（1989），395---424）研究使用$ J $ - 旋球曲线的等距沉浸液。由于亨氏和Pogorelov引起的经典定理的概括，我们获得了。
We revisit the classical problem due to Weyl, as well as its generalisations, concerning the isometric immersions of $\mathbb{S}^2$ into simply-connected $3$-dimensional Riemannian manifolds with non-negative Gauss curvature. A sufficient condition is exhibited for the existence of global $C^{1,1}$-isometric immersions. Our developments are based on the framework à la Labourie (Immersions isométriques elliptiques et courbes pseudo-holomorphes, J. Diff. Geom. 30 (1989), 395--424) of studying isometric immersions using $J$-holomorphic curves. We obtain along the way a generalisation of a classical theorem due to Heinz and Pogorelov.
