تقرير
Hausdorff limits of submanifolds of symplectic and contact manifolds
| العنوان: | Hausdorff limits of submanifolds of symplectic and contact manifolds |
|---|---|
| المؤلفون: | Chassé, Jean-Philippe |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Symplectic Geometry, Mathematics - Differential Geometry, Mathematics - Metric Geometry, 53D12 (Primary), 53D05, 53D10, 53C17 (Secondary) |
| الوصف: | 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. Comment: 31 pages, 0 figure. Added a new part in the statement of Theorem A for nonexact Lagrangians and a new corollary to it (now Corollary 2); improved the presentation of the results and fixed a small error in the proof of Proposition 2 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2204.02468 |
| رقم الأكسشن: | edsarx.2204.02468 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |