Results 1 
6 of
6
Hyperbolic geometry
 In Flavors of geometry
, 1997
"... 3. Why Call it Hyperbolic Geometry? 63 4. Understanding the OneDimensional Case 65 ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
3. Why Call it Hyperbolic Geometry? 63 4. Understanding the OneDimensional Case 65
Endomorphisms of Kleinian groups
 Geom. Funct. Anal
"... A group G is cohopan (or has the coHopf property) if any injective endomorphism f: G! G is surjective. Answering a question of E. Rips, Z. Sela showed in [Se] that a torsionfree, non virtually cyclic wordhyperbolic group (in Gromov's sense) is cohopan if and only if it is not a nontrivial f ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
(Show Context)
A group G is cohopan (or has the coHopf property) if any injective endomorphism f: G! G is surjective. Answering a question of E. Rips, Z. Sela showed in [Se] that a torsionfree, non virtually cyclic wordhyperbolic group (in Gromov's sense) is cohopan if and only if it is not a nontrivial free
The Uniform Norm of Hyperinterpolation on the Unit Sphere in an Arbitrary Number of Dimensions
, 2000
"... In this paper, we study the order of growth of the uniform norm of the hyperinterpolation operator on the unit sphere S r1 # IR r . The hyperinterpolation approximation Ln f , where f # C(S r1 ), is derived from the exact L 2 orthogonal projection #n f onto the space P r n (S r1 ) ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
In this paper, we study the order of growth of the uniform norm of the hyperinterpolation operator on the unit sphere S r1 # IR r . The hyperinterpolation approximation Ln f , where f # C(S r1 ), is derived from the exact L 2 orthogonal projection #n f onto the space P r n (S r1 ) of spherical polynomials of degree n or less, with the Fourier coe#cients approximated by a positive weight quadrature rule that integrates exactly all polynomials of degree # 2n. We extend to arbitrary r the recent r = 3 result of Sloan and Womersley [9], by proving that under an additional "quadrature regularity" assumption on the quadrature rule, the order of growth of the uniform norm of the hyperinterpolation operator on the unit sphere is O(n r/21 ), which is the same as that of the orthogonal projection #n , and best possible among all linear projections onto P r n (S r1 ). Key words: hyperinterpolation, interpolation, reproducing kernel, unit sphere. AMS Subject Classifica...
CROSS CURVATURE FLOW ON A NEGATIVELY CURVED SOLID TORUS
"... Abstract. The classic 2πTheorem of Gromov and Thurston constructs a negatively curved metric on certain 3manifolds obtained by Dehn filling. By Geometrization, any such manifold admits a hyperbolic metric. We outline a program using cross curvature flow to construct a smooth oneparameter family o ..."
Abstract
 Add to MetaCart
Abstract. The classic 2πTheorem of Gromov and Thurston constructs a negatively curved metric on certain 3manifolds obtained by Dehn filling. By Geometrization, any such manifold admits a hyperbolic metric. We outline a program using cross curvature flow to construct a smooth oneparameter family of metrics between the “2πmetric ” and the hyperbolic metric. We make partial progress in the program, proving longtime existence, preservation of negative sectional curvature, curvature bounds, and integral convergence to hyperbolic for the metrics under consideration. 1.
Horotight immersions of S1
"... We characterize horotight immersions into Dm in terms of a family of real valued functions parametrized by Sm1. By means of such functions we provide an elementary proof that horotightness and tightness are equivalent properties in the class of immersions from S1 into hyperbolic space. May, 2005 I ..."
Abstract
 Add to MetaCart
(Show Context)
We characterize horotight immersions into Dm in terms of a family of real valued functions parametrized by Sm1. By means of such functions we provide an elementary proof that horotightness and tightness are equivalent properties in the class of immersions from S1 into hyperbolic space. May, 2005 ICMCUSP 1.
Repeated Compositions of Analytic Maps
"... Abstract. Given a sequence fj of analytic maps of the open unit disc D into itself, we consider conditions that guarantee that the sequence f1 ± ¢ ¢ ¢ ± fn of compositions converges uniformly on D to a constant. The proofs are given entirely in terms of two and threedimensional hyperbolic geome ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. Given a sequence fj of analytic maps of the open unit disc D into itself, we consider conditions that guarantee that the sequence f1 ± ¢ ¢ ¢ ± fn of compositions converges uniformly on D to a constant. The proofs are given entirely in terms of two and threedimensional hyperbolic geometry.