Results 21 to 30 of about 87 (78)

A new characterization of Gromov hyperbolicity for negatively curved surfaces [PDF]

, 2006
23 pages, no figures.-- MSC2000 codes: 53C23, 30F20, 30F45.MR#: MR2273661 (2007j:53046)Zbl#: Zbl 1111.53033In this paper we show that to check Gromov hyperbolicity of any surface of constant negative curvature, or, Riemann surface, we only need to verify
Tourís, Eva, Rodríguez, José M.
core   +1 more source

Asymptotically Mean Value Harmonic Functions in Doubling Metric Measure Spaces

Analysis and Geometry in Metric Spaces, 2022
We consider functions with an asymptotic mean value property, known to characterize harmonicity in Riemannian manifolds and in doubling metric measure spaces.
Adamowicz Tomasz, Kijowski Antoni, Soultanis Elefterios   +2 more
doaj   +1 more source

A characterization of Gromov hyperbolicity of surfaces with variable negative curvature [PDF]

, 2009
18 pages, 4 figures.-- MSC2000 codes: 53C15, 53C21, 53C22, 53C23.MR#: MR2474116 (2009k:53091)Zbl#: Zbl 1153.53320In this paper we show that, in order to check Gromov hyperbolicity of any surface with curvature $K \leq -k^2 < 0$, we just need to verify ...
Tourís, Eva, Portilla, Ana
core   +1 more source

Stability of Gromov hyperbolicity [PDF]

, 2009
20 pages, 1 figure.-- MSC2000 codes: 30F45; 53C23, 30C99.Zbl#: Zbl pre05652685A main problem when studying any mathematical property is to determine its stability, i.e., under what type of perturbations it is preserved.
Tourís, Eva, Rodríguez, José M., Portilla, Ana   +2 more
core   +3 more sources

SPACE OF RICCI FLOWS (II)—PART A: MODULI OF SINGULAR CALABI–YAU SPACES

Forum of Mathematics, Sigma, 2017
We establish the compactness of the moduli space of noncollapsed Calabi–Yau spaces with mild singularities. Based on this compactness result, we develop a new approach to study the weak compactness of Riemannian manifolds.
XIUXIONG CHEN, BING WANG
doaj   +1 more source

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

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