Results 1  10
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17
NONSMOOTH CALCULUS
"... Abstract. We survey recent advances in analysis and geometry, where first order differential analysis has been extended beyond its classical smooth settings. Such studies have applications to geometric rigidity questions, but are also of intrinsic interest. The transition from smooth spaces to singu ..."
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Abstract. We survey recent advances in analysis and geometry, where first order differential analysis has been extended beyond its classical smooth settings. Such studies have applications to geometric rigidity questions, but are also of intrinsic interest. The transition from smooth spaces to singular spaces where calculus is possible parallels the classical development from smooth functions to functions with weak or generalized derivatives. Moreover, there is a new way of looking at the classical geometric theory of Sobolev functions that is useful in more general contexts. 1.
Spaces and groups with conformal dimension greater than one
, 2010
"... Abstract. We show that if a complete, doubling metric space is annularly linearly connected then its conformal dimension is greater than one, quantitatively. As a consequence, we answer a question of Bonk and Kleiner: if the boundary of a oneended hyperbolic group has no local cut points, then its ..."
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Abstract. We show that if a complete, doubling metric space is annularly linearly connected then its conformal dimension is greater than one, quantitatively. As a consequence, we answer a question of Bonk and Kleiner: if the boundary of a oneended hyperbolic group has no local cut points, then its conformal dimension is greater than one. 1.
CONFORMAL DIMENSION AND RANDOM GROUPS
"... Abstract. We give a lower and an upper bound for the conformal dimension of the boundaries of certain small cancellation groups. We apply these bounds to the few relator and density models for random groups. This gives generic bounds of the following form, where l is the relator length, going to inf ..."
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Abstract. We give a lower and an upper bound for the conformal dimension of the boundaries of certain small cancellation groups. We apply these bounds to the few relator and density models for random groups. This gives generic bounds of the following form, where l is the relator length, going to infinity. (a) 1 + 1/C < Cdim(∂∞G) < Cl / log(l), for the few relator model, and (b) 1 + l/(C log(l)) < Cdim(∂∞G) < Cl, for the density model, at densities d < 1/16. In particular, for the density model at densities d < 1/16, as the relator length l goes to infinity, the random groups will pass through infinitely many different quasiisometry classes. 1.
Spaces with conformal dimension greater than one
, 2007
"... Abstract. We show that if a complete, doubling metric space is annulus linearly connected then its conformal dimension is greater than one, quantitatively. As a consequence, hyperbolic groups whose boundaries have no local cut points have conformal dimension greater than one; this answers a question ..."
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Cited by 2 (1 self)
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Abstract. We show that if a complete, doubling metric space is annulus linearly connected then its conformal dimension is greater than one, quantitatively. As a consequence, hyperbolic groups whose boundaries have no local cut points have conformal dimension greater than one; this answers a question of Bonk and Kleiner. 1.
Nica: Finitely summable Fredholm modules for boundary actions of hyperbolic groups
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ON GROUPS WITH LINEAR SCI GROWTH
"... Abstract. We prove that the simple connectivity at infinity growth of sci hyperbolic groups and most nonuniform lattices is linear. Using the fact that the enddepth of finitely presented groups is linear we prove that the linear growth of simple connectivity at infinity is preserved under amalgama ..."
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Abstract. We prove that the simple connectivity at infinity growth of sci hyperbolic groups and most nonuniform lattices is linear. Using the fact that the enddepth of finitely presented groups is linear we prove that the linear growth of simple connectivity at infinity is preserved under amalgamated products over finitely generated oneended groups.
1 Quasiisometry rigidity for hyperbolic buildings
"... We summarize BoundonPajot’s quasiisometry rigidity for some negativelycurved buildings. 1.1 ..."
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We summarize BoundonPajot’s quasiisometry rigidity for some negativelycurved buildings. 1.1