Compact embedded minimal surfaces in $\mathbb{S}^2 \times \mathbb{S}^1$
نویسندگان
چکیده
منابع مشابه
Compact Embedded Minimal Surfaces of Positive Genus without Area Bounds
LetM be a three-manifold (possibly with boundary). We will show that, for any positive integer γ, there exists an open nonempty set of metrics on M (in the C-topology on the space of metrics on M) for each of which there are compact embedded stable minimal surfaces of genus γ with arbitrarily large area. This extends a result of Colding and Minicozzi, who proved the case γ = 1.
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The study of embedded minimal surfaces in R is a classical problem, dating to the mid 1700’s, and many people have made key contributions. We will survey a few recent advances, focusing on joint work with Tobias H. Colding of MIT and Courant, and taking the opportunity to focus on results that have not been highlighted elsewhere. Mathematics Subject Classification (2000). Primary 53A10; Seconda...
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Surfaces that locally minimize area have been extensively used to model physical phenomena, including soap films, black holes, compound polymers, protein folding, etc. The mathematical field dates to the 1740s but has recently become an area of intense mathematical and scientific study, specifically in the areas of molecular engineering, materials science, and nanotechnology because of their ma...
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In this short paper, we apply estimates and ideas from [CM4] to study the ends of a properly embedded complete minimal surface 2 ⊂ R3 with finite topology. The main result is that any complete properly embedded minimal annulus that lies above a sufficiently narrow downward sloping cone must have finite total curvature. In this short paper, we apply estimates and ideas from [CM4] to study the en...
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ژورنال
عنوان ژورنال: Communications in Analysis and Geometry
سال: 2016
ISSN: 1019-8385,1944-9992
DOI: 10.4310/cag.2016.v24.n2.a7