تقرير
On the spectrum and index of expanding and translating solitons of the mean curvature flow in $\mathbb{R}^3$
| العنوان: | On the spectrum and index of expanding and translating solitons of the mean curvature flow in $\mathbb{R}^3$ |
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| المؤلفون: | Alencar, Hilário, Neto, Gregório Silva |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, Mathematics - Analysis of PDEs, Primary 53E10, 53C42, 53C21, Secondary 35C06, 35A15, 35A23, 35J15, 35J60 |
| الوصف: | In this paper we prove that two-dimensional translating solitons in $\mathbb{R}^3$ with finite $L$-index are homeomorphic to a plane or a cylinder and that a two-dimensional self-expander with finite $L$-index and sub exponential weighted volume growth has finite topology. We also prove that translating solitons and self-expanders have finite topology, provided the bottom of the spectrum of the $L$-stability operator is bounded from below and their weighted volume have subexponential growth. Comment: We made a mistake in the proof of Lemma 2.5, we thanks PR. M\'arcio Batista (UFAL) for pointed us out this |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2203.06214 |
| رقم الأكسشن: | edsarx.2203.06214 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |