Results 1 to 10 of about 754 (96)

A note on the almost-Schur lemma on smooth metric measure spaces. [PDF]

J Inequal Appl, 2018
In this paper, we prove almost Schur Lemma on closed smooth metric measure spaces, which implies the results of X.
Chen JT.
europepmc   +2 more sources

5-Point CAT(0) Spaces after Tetsu Toyoda

Analysis and Geometry in Metric Spaces, 2021
We give another proof of Toyoda’s theorem that describes 5-point subspaces in CAT(0) length spaces.
Anton Petrunin
exaly   +2 more sources

Remarks on Manifolds with Two-Sided Curvature Bounds

Analysis and Geometry in Metric Spaces, 2021
We discuss folklore statements about distance functions in manifolds with two-sided bounded curvature. The topics include regularity, subsets of positive reach and the cut locus.
Kapovitch Vitali, Lytchak Alexander
exaly   +2 more sources

Stable systolic category of the product of spheres [PDF]

, 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   +2 more sources

A New Transport Distance and Its Associated Ricci Curvature of Hypergraphs

Analysis and Geometry in Metric Spaces, 2022
The coarse Ricci curvature of graphs introduced by Ollivier as well as its modification by Lin–Lu– Yau have been studied from various aspects. In this paper, we propose a new transport distance appropriate for hypergraphs and study a generalization of ...
Akamatsu Tomoya
doaj   +1 more source

Quasihyperbolic mappings in length metric spaces

, 2021
In this paper, we discuss the local properties of quasihyperbolic mappings in metric spaces, which are related to an open problem raised by Huang et al in 2016.
Qingshan Zhou, Yaxiang Li, Yuehui He
semanticscholar   +1 more source

Extremal subsets in geodesically complete spaces with curvature bounded above

Analysis and Geometry in Metric Spaces, 2023
We introduce the notion of an extremal subset in a geodesically complete space with curvature bounded above, i.e., a GCBA space. This is an analog of an extremal subset in an Alexandrov space with curvature bounded below introduced by Perelman and ...
Fujioka Tadashi
doaj   +1 more source

Widths of balls and free boundary minimal submanifolds

Advanced Nonlinear Studies, 2023
We observe that the kk-dimensional width of an nn-ball in a space form is given by the area of an equatorial kk-ball. We also discuss the relationship between widths and lower bounds for the area of a free boundary minimal submanifold in a space form ...
Zhu Jonathan J.
doaj   +1 more source

Lipschitz Chain Approximation of Metric Integral Currents

Analysis and Geometry in Metric Spaces, 2022
Every integral current in a locally compact metric space X can be approximated by a Lipschitz chain with respect to the normal mass, provided that Lipschitz maps into X can be extended slightly.
Goldhirsch Tommaso
doaj   +1 more source

Simplicial volume of Hilbert modular varieties [PDF]

, 2007
The simplicial volume introduced by Gromov provides a topologically accessible lower bound for the minimal volume. Lafont and Schmidt proved that the simplicial volume of closed, locally symmetric spaces of non-compact type is positive. In this paper, we
C. Loeh, Roman Sauer
semanticscholar   +1 more source