تقرير
Helicoidal surfaces of prescribed mean curvature in $\mathbb{R}^3$
| العنوان: | Helicoidal surfaces of prescribed mean curvature in $\mathbb{R}^3$ |
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| المؤلفون: | Barbieri, Aires Eduardo Menani |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, 53A10, 53C42, 34C05, 34C40 |
| الوصف: | Given a function $\mathcal{H} \in C^1(\mathbb{S}^2)$, an $\mathcal{H}$-surface $\Sigma$ is a surface in the Euclidean space $\mathbb{R}^3$ whose mean curvature $H_\Sigma$ satisfies $H_\Sigma = \mathcal{H} \circ \eta$, where $\eta$ is the Gauss map of $\Sigma$. The purpose of this paper is to use a phase space analysis to give some classification results for helicoidal $\mathcal{H}$-surfaces, when $\mathcal{H}$ is rotationally symmetric, that is, $\mathcal{H} \circ \eta = \mathfrak{h} \circ \nu$, for some $\mathfrak{h} \in C^1([-1,1])$, where $\nu$ is the angle function of the surface. We prove a classification theorem for the case where $\mathfrak{h}(t)$ is even and increasing for $t \in [0,1]$. Finally, we provide examples of helicoidal $\mathcal{H}$-surfaces in cases where $\mathfrak{h}$ vanishes at some point. Comment: 27 pages, 18 figures. arXiv admin note: text overlap with arXiv:1902.09405 by other authors |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2401.04721 |
| رقم الأكسشن: | edsarx.2401.04721 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |