منابع مشابه
Properly embedded minimal planar domains with infinite topology are Riemann minimal examples
These notes outline recent developments in classical minimal surface theory that are essential in classifying the properly embedded minimal planar domains M ⊂ R with infinite topology (equivalently, with an infinite number of ends). This final classification result by Meeks, Pérez, and Ros [64] states that such an M must be congruent to a homothetic scaling of one of the classical examples foun...
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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...
متن کاملOn Properly Embedded Minimal Surfaces with Three Ends
We classify all complete embedded minimal surfaces in R3 with three ends of genus g and at least 2g + 2 symmetries. The surfaces in this class are the Costa-HoffmanMeeks surfaces that have 4g + 4 symmetries in the case of a flat middle end. The proof consists of using the symmetry assumptions to deduce the possible Weierstrass data and then studying the period problems in all cases. To handle t...
متن کاملThe Space of Embedded Minimal Surfaces of Fixed Genus in a 3-manifold Iii; Planar Domains
This paper is the third in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed 3-manifold. In [CM3]–[CM5] we describe the case where the surfaces are topologically disks on any fixed small scale (in fact, Corollary III.3.5 below is used in [CM5]). To describe general planar domains (in [CM6]) we need in addition to the results o...
متن کاملMinimal Connected Enclosures on an Embedded Planar Graph
We study ve problems of nding minimal enclosures comprised of elements of a connected, planar graph with a plane embedding. The rst three problems consider the identiication of a shortest enclosing walk, cycle or trail surrounding a polygonal, simply connected obstacle on the plane. We propose polynomial algorithms that improve over existing algorithms. The last two problems consider the format...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2015
ISSN: 0003-486X
DOI: 10.4007/annals.2015.181.2.2