Results 31 to 40 of about 695 (57)

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

Stable systolic category of the product of spheres

, 2010
The stable systolic category of a closed manifold M indicates the complexity in the sense of volume. This is a homotopy invariant, even though it is defined by some relations between homological volumes on M.
Berger, Federer, Gromov, Hoil Ryu
core   +1 more source

A short proof of Gromov's filling inequality

, 2007
We give a very short and rather elementary proof of Gromov's filling volume inequality for n-dimensional Lipschitz cycles (with integer and Z_2-coefficients) in $L^\infty$-spaces.
Wenger, Stefan
core   +3 more sources

Measurements of Riemannian two-disks and two-spheres

, 2014
We prove that any Riemannian two-sphere with area at most 1 can be continuously mapped onto a tree in a such a way that the topology of fibers is controlled and their length is less than 7.6.
Balacheff, Florent
core   +1 more source

Intrinsic flat convergence with bounded Ricci curvature [PDF]

, 2015
In this paper we address the relationship between Gromov-Hausdorff limits and intrinsic flat limits of complete Riemannian manifolds. In \cite{SormaniWenger2010, SormaniWenger2011}, Sormani-Wenger show that for a sequence of Riemannian manifolds with ...
Munn, Michael
core  

Enlargeable metrics on nonspin manifolds

, 2019
We show that an enlargeable Riemannian metric on a (possibly nonspin) manifold cannot have uniformly positive scalar curvature. This extends a well-known result of Gromov and Lawson to the nonspin setting.
Cecchini, Simone, Schick, Thomas
core   +1 more source

A parametrized compactness theorem under bounded Ricci curvature

, 2017
We prove a parametrized compactness theorem on manifolds of bounded Ricci curvature, upper bounded diameter and lower bounded injectivity radius.Comment: 17 pages. Final version to appear in Front. Math. China. Reformulation of Theorem B to Corollary 1,
Li, Xiang, Xu, Shicheng
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

Curvature exponent and geodesic dimension on Sard-regular Carnot groups

Analysis and Geometry in Metric Spaces
In this study, we characterize the geodesic dimension NGEO{N}_{{\rm{GEO}}} and give a new lower bound to the curvature exponent NCE{N}_{{\rm{CE}}} on Sard-regular Carnot groups.
Golo Sebastiano Nicolussi, Zhang Ye
doaj   +1 more source