تقرير
Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds
| العنوان: | Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds |
|---|---|
| المؤلفون: | Deruelle, Alix, Schulze, Felix, Simon, Miles |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, Mathematics - Analysis of PDEs |
| الوصف: | This paper investigates the question of stability for a class of Ricci flows which start at possibly non-smooth metric spaces. We show that if the initial metric space is Reifenberg and locally bi-Lipschitz to Euclidean space, then two solutions to the Ricci flow whose Ricci curvature is uniformly bounded from below and whose curvature is bounded by $c\cdot t^{-1}$ converge to one another at an exponential rate once they have been appropriately gauged. As an application, we show that smooth three dimensional, complete, uniformly Ricci-pinched Riemannian manifolds with bounded curvature are either compact or flat, thus confirming a conjecture of Hamilton and Lott. Comment: 41 pages, comments welcome! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2203.15313 |
| رقم الأكسشن: | edsarx.2203.15313 |
| قاعدة البيانات: | arXiv |
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