Asymptotic curvature ratio, nonnegative curvature and non-collapsing

Alix Deruelle[1]

  • [1] Institut Fourier, Université de Grenoble I 38402 Saint-Martin d’Hères, France

Séminaire de théorie spectrale et géométrie (2011-2012)

  • Volume: 30, page 47-75
  • ISSN: 1624-5458

Abstract

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We focus on a geometric invariant associated to any noncompact Riemannian manifold : the asymptotic curvature ratio introduced by Gromov. We study how it interacts with the topology of the underlying manifold with other geometric constraints such as positive asymptotic volume ratio, nonnegative (Ricci) curvature and finiteness of the fundamental group (at infinity).

How to cite

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Deruelle, Alix. "Rapport asymptotique de courbure, courbure positive et non effondrement." Séminaire de théorie spectrale et géométrie 30 (2011-2012): 47-75. <http://eudml.org/doc/275728>.

@article{Deruelle2011-2012,
abstract = {On s’intéresse ici à un invariant géométrique associé à toute variété riemannienne non compacte : le rapport asymptotique de courbure. On étudie son influence sur la topologie de la variété sous-jacente en présence d’autres contraintes géométrico-topologiques portant sur le volume asymptotique, la positivité de la courbure (de Ricci) et/ou la finitude du groupe fondamental (à l’infini).},
affiliation = {Institut Fourier, Université de Grenoble I 38402 Saint-Martin d’Hères, France},
author = {Deruelle, Alix},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {Riemannian geometry; nonnegative curvature; asymptotic cone; collapsing at infinity; topology of noncompact Riemannian manifolds},
language = {fre},
pages = {47-75},
publisher = {Institut Fourier},
title = {Rapport asymptotique de courbure, courbure positive et non effondrement},
url = {http://eudml.org/doc/275728},
volume = {30},
year = {2011-2012},
}

TY - JOUR
AU - Deruelle, Alix
TI - Rapport asymptotique de courbure, courbure positive et non effondrement
JO - Séminaire de théorie spectrale et géométrie
PY - 2011-2012
PB - Institut Fourier
VL - 30
SP - 47
EP - 75
AB - On s’intéresse ici à un invariant géométrique associé à toute variété riemannienne non compacte : le rapport asymptotique de courbure. On étudie son influence sur la topologie de la variété sous-jacente en présence d’autres contraintes géométrico-topologiques portant sur le volume asymptotique, la positivité de la courbure (de Ricci) et/ou la finitude du groupe fondamental (à l’infini).
LA - fre
KW - Riemannian geometry; nonnegative curvature; asymptotic cone; collapsing at infinity; topology of noncompact Riemannian manifolds
UR - http://eudml.org/doc/275728
ER -

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