论文标题
Sumphectic和接触歧管的子手机的Hausdorff极限
Hausdorff limits of submanifolds of symplectic and contact manifolds
论文作者
论文摘要
我们研究了尊重来自Riemannian几何形状界限的沉浸式序列，并将随之而来的结果应用于对符号和接触歧管的亚序列序列的研究。这使我们能够研究Hausdorff指标与拉格朗日Hofer和光谱指标之间的微妙相互作用。在此过程中，我们获得了附近拉格朗日猜想的度量版本和光谱规范上的Viterbo猜想的证明。在存在Riemannian界限的情况下，我们还获得了一类符号和触点歧管的大量重要子手法的$ c^0 $ - 条件结果。同样，我们在同时$ c^0 $以及HOFER/SPESTRAL LIMITS上的Hofer和Viterbo的结果得到了拉格朗日的概括〜 -〜即使没有任何此类界限。
We study sequences of immersions respecting bounds coming from Riemannian geometry and apply the ensuing results to the study of sequences of submanifolds of symplectic and contact manifolds. This allows us to study the subtle interaction between the Hausdorff metric and the Lagrangian Hofer and spectral metrics. In the process, we get proofs of metric versions of the nearby Lagrangian conjecture and of the Viterbo conjecture on the spectral norm. We also get $C^0$-rigidity results for a vast class of important submanifolds of symplectic and contact manifolds in the presence of Riemannian bounds. Likewise, we get a Lagrangian generalization of results of Hofer and Viterbo on simultaneous $C^0$ and Hofer/spectral limits~ -- ~even without any such bounds.
