Results 31 to 40 of about 731 (76)

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

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

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  

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

Resolvent Flows for Convex Functionals and p-Harmonic Maps

Analysis and Geometry in Metric Spaces, 2015
We prove the unique existence of the (non-linear) resolvent associated to a coercive proper lower semicontinuous function satisfying a weak notion of p-uniform λ-convexity on a complete metric space, and establish the existence of the minimizer of such ...
Kuwae Kazuhiro
doaj   +1 more source