تقرير
On the Hamilton-Lott conjecture in higher dimensions
| العنوان: | On the Hamilton-Lott conjecture in higher dimensions |
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| المؤلفون: | Deruelle, Alix, Schulze, Felix, Simon, Miles |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, Mathematics - Analysis of PDEs |
| الوصف: | We study $n$-dimensional Ricci flows with non-negative Ricci curvature where the curvature is pointwise controlled by the scalar curvature and bounded by $C/t$, starting at metric cones which are Reifenberg outside the tip. We show that any such flow behaves like a self-similar solution up to an exponential error in time. As an application, we show that smooth $n$-dimensional complete non-compact Riemannian manifolds which are uniformly PIC1-pinched, with positive asymptotic volume ratio, are Euclidean. This confirms a higher dimensional version of a conjecture of Hamilton and Lott under the assumption of non-collapsing. It also yields a new and more direct proof of the original conjecture of Hamilton and Lott in three dimensions. Comment: 34 pages, introduction slightly extended and references updated |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.00708 |
| رقم الأكسشن: | edsarx.2403.00708 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |