Results 31 to 40 of about 754 (96)

Volume Bounds for the Quantitative Singular Strata of Non Collapsed RCD Metric Measure Spaces

Analysis and Geometry in Metric Spaces, 2019
The aim of this note is to generalize to the class of non collapsed RCD(K, N) metric measure spaces the volume bound for the effective singular strata obtained by Cheeger and Naber for non collapsed Ricci limits in [13].
Antonelli Gioacchino, Brué Elia, Semola Daniele   +2 more
doaj   +1 more source

Pontryagin numbers and nonnegative curvature

, 2010
We prove that any rational linear combination of Pontryagin numbers that is not a multiple of the signature is unbounded on connected closed oriented manifolds of nonnegative sectional curvature.
Kotschick, D.
core   +1 more source

Chordal Hausdorff Convergence and Quasihyperbolic Distance

Analysis and Geometry in Metric Spaces, 2020
We study Hausdorff convergence (and related topics) in the chordalization of a metric space to better understand pointed Gromov-Hausdorff convergence of quasihyperbolic distances (and other conformal distances).
Herron David A., Richard Abigail, Snipes Marie A.   +2 more
doaj   +1 more source

An Intrinsic Characterization of Five Points in a CAT(0) Space

Analysis and Geometry in Metric Spaces, 2020
Gromov (2001) and Sturm (2003) proved that any four points in a CAT(0) space satisfy a certain family of inequalities. We call those inequalities the ⊠-inequalities, following the notation used by Gromov.
Toyoda Tetsu
doaj   +1 more source

Bounded characteristic classes and flat bundles

, 2012
Let G be a connected Lie group, G^d the underlying discrete group, and BG, BG^d their classifying spaces. Let R denote the radical of G. We show that all classes in the image of the canonical map in cohomology H^*(BG,R)->H^*(BG^d,R) are bounded if and ...
Chatterji, Indira, Cornulier, Yves, Mislin, Guido, Pittet, Christophe   +3 more
core   +4 more sources

An optimal systolic inequality for CAT(0) metrics in genus two

, 2006
We prove an optimal systolic inequality for CAT(0) metrics on a genus~2 surface. We use a Voronoi cell technique, introduced by C.~Bavard in the hyperbolic context. The equality is saturated by a flat singular metric in the conformal class defined by the
Katz, Mikhail G., Sabourau, Stephane
core   +2 more sources

Quantitative Rellich Inequalities on Finsler-Hadamard Manifolds

, 2016
In this paper we are dealing with quantitative Rellich inequalities on Finsler-Hadamard manifolds where the remainder terms are expressed by means of the flag curvature.
Kristály, Alexandru, Repovš, Dušan
core   +1 more source

Simplicial volume of Q-rank one locally symmetric manifolds covered by the product of R-rank one symmetric spaces

, 2012
In this paper, we show that the simplicial volume of Q-rank one locally symmetric spaces covered by the product of R-rank one symmetric spaces is strictly ...
Borel, Connell, Connell, Connell, Eberlein, Gromov, Inkang Kim, Sungwoon Kim, Zimmer   +8 more
core   +1 more source

Degrees of maps and multiscale geometry

Forum of Mathematics, Pi
We study the degree of an L-Lipschitz map between Riemannian manifolds, proving new upper bounds and constructing new examples. For instance, if $X_k$ is the connected sum of k copies of $\mathbb CP^2$ for $k \ge 4$ , then we prove ...
Aleksandr Berdnikov, Larry Guth, Fedor Manin   +2 more
doaj   +1 more source

Contractibility of boundaries of cocompact convex sets and embeddings of limit sets

Analysis and Geometry in Metric Spaces
We provide sufficient conditions as to when a boundary component of a cocompact convex set in a CAT(0){\rm{CAT}}\left(0)-space is contractible. We then use this to study when the limit set of a quasi-convex, codimension one subgroup of a negatively ...
Bregman Corey, Incerti-Medici Merlin
doaj   +1 more source