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Classification of tilings of the 2dimensional sphere by congruent triangles
 Hiroshima Math. J
, 2002
"... We give a new classification of tilings of the 2dimensional sphere by congruent triangles accompanied with a complete proof. This accomplishes the old classification by Davies, who only gave an outline of the proof, regrettably with some redundant tilings. We clarify Davies ’ obscure points, give a ..."
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Cited by 16 (0 self)
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We give a new classification of tilings of the 2dimensional sphere by congruent triangles accompanied with a complete proof. This accomplishes the old classification by Davies, who only gave an outline of the proof, regrettably with some redundant tilings. We clarify Davies ’ obscure points, give
The length of a shortest closed geodesic and the area of a 2dimensional sphere
 Proc. Amer. Math. Soc
"... Abstract. Let M be a Riemannian manifold homeomorphic to S 2. The purpose of this paper is to establish the new inequality for the length of a shortest closed geodesic, l(M), in terms of the area A of M. This result improves previously known inequalities by C.B. Croke (1988), by A. Nabutovsky and th ..."
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Cited by 12 (1 self)
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and the author (2002) and by S. Sabourau (2004). Let l(M) denote the length of a shortest closed nontrivial geodesic on a closed Riemannian manifold M and let A be the area of M. In this paper we will prove the following theorem. Theorem 0.1. Let M be a manifold diffeomorphic to the 2dimensional sphere. Then l
Homogeneous polynomial vector fields of degree 2 on the 2– dimensional sphere, preprint
, 2006
"... Abstract Let X be a homogeneous polynomial vector field of degree 2 on S 2 having finitely many invariant circles. Then, we prove that each invariant circle is a great circle of S 2 , and at most there are two invariant circles. We characterize the global phase portrait of these vector fields. More ..."
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Abstract Let X be a homogeneous polynomial vector field of degree 2 on S 2 having finitely many invariant circles. Then, we prove that each invariant circle is a great circle of S 2 , and at most there are two invariant circles. We characterize the global phase portrait of these vector fields
Darbouxian integrability for polynomial vector fields on the 2dimensional sphere, Extracta Mathematicae 17
, 2002
"... In 1878 Darboux [6] showed how can be constructed the first integrals of planar polynomial vector fields possessing sufficient invariant algebraic curves. In particular, he proved that if a planar polynomial vector field of degree m has at least [m(m + 1)/2] + 1 invariant algebraic curves, then it h ..."
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Cited by 2 (2 self)
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In 1878 Darboux [6] showed how can be constructed the first integrals of planar polynomial vector fields possessing sufficient invariant algebraic curves. In particular, he proved that if a planar polynomial vector field of degree m has at least [m(m + 1)/2] + 1 invariant algebraic curves
CMC–Surfaces, ϕ–Geodesics and
, 2008
"... A short proof of the Caratheodory conjecture about index of an isolated umbilic on the convex 2–dimensional sphere is suggested. ..."
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A short proof of the Caratheodory conjecture about index of an isolated umbilic on the convex 2–dimensional sphere is suggested.
Hiroshima Math. J. 35 (2005), 93–113 Stable maps between 2spheres with a connected fold curve
, 2003
"... Abstract. Stable maps between 2dimensional spheres, whose fold curve is connected and its image is simple with minimal number of cusps, are classified for every degree db 2. 1. ..."
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Abstract. Stable maps between 2dimensional spheres, whose fold curve is connected and its image is simple with minimal number of cusps, are classified for every degree db 2. 1.
Equidistribution on the Sphere
 SIAM J. Sci. Stat. Comput
, 1997
"... A concept of generalized discrepancy, which involves pseudodifferential operators to give a criterion of equidistributed pointsets, is developed on the sphere. A simply structured formula in terms of elementary functions is established for the computation of the generalized discrepancy. With the hel ..."
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Cited by 32 (2 self)
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. With the help of this formula five kinds of point systems on the sphere, namely lattices in polar coordinates, transformed 2dimensional sequences, rotations on the sphere, triangulation, and "sum of three squares sequence", are investigated. Quantitative tests are done, and the results are compared
Real algebraic morphisms on 2dimensional conic bundles
 Adv. Geom
"... Abstract. Given two nonsingular real algebraic varieties V and W, we consider the problem of deciding whether a smooth map f: V → W can be approximated by regular maps in the space of C ∞ mappings from V to W in the C ∞ topology. Our main result is a complete solution to this problem in case W is th ..."
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Cited by 8 (5 self)
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is the usual 2dimensional sphere and V is a real algebraic surface of negative Kodaira dimension. 1.
Minimizing the discrete logarithmic energy on the sphere: the role of random polynomials
 Trans. Amer. Math. Soc
"... Abstract. We prove that points in the sphere associated with roots of random polynomials via the stereographic projection are surprisingly wellsuited with respect to the minimal logarithmic energy on the sphere. That is, roots of random polynomials provide a fairly good approximation to elliptic Fe ..."
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Cited by 10 (2 self)
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Fekete points. This paper deals with the problem of distributing points in the 2dimensional sphere, in a way that the logarithmic energy is minimized. More precisely, let x1,..., xN ∈ R3, and let (0.1) V (x1,..., xN) = ln
Nesting Points in the Sphere
 Discrete Mathematics
, 1999
"... Let G be a graph embedded in the sphere. A knest of a point x not in G is a collection C 1 ; : : : ; C k of disjoint cycles such that for each C i , the side contain x also contains C j for each j ! i. An embedded graph is knested if each point not on the graph has a knest. In this paper we e ..."
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@delta.cs.cinvestav.mx 1 1 Introduction Let G be a spherical graph, a graph drawn without crossings on the 2dimensional sphere S. Our interest is in separating some points in the sphere from others using simple cycles in G. Of course, this is not always possible: two points in the same component, or same face
Results 1  10
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1,737