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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

Some Convergence Theorems of Modified Proximal Point Algorithms for Nonexpansive Mappings in CAT(0) Spaces [PDF]

Results in Nonlinear Analysis, 2018
In this paper, a new modified proximal point algorithm is proposed for finding a common element of the set of fixed points of a single-valued nonexpansive mapping, and the set of fixed points of a multivalued nonexpansive mapping, and the set of ...
Shengquan Weng , Dingping Wu
doaj  

A Generalization of Suzuki's Lemma

Abstract and Applied Analysis, 2011
Let {zn}, {wn}, and {vn} be bounded sequences in a metric space of hyperbolic type (X,d), and let {αn} be a sequence in [0,1] with ...
B. Panyanak, A. Cuntavepanit
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An Application of Proof Mining to the Proximal Point Algorithm in CAT(0) Spaces [PDF]

, 2018
Laurenţiu Leuştean, Andrei Sipoş
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Some Convergence Theorems for Contractive Type Mappings in CAT(0) Spaces

Abstract and Applied Analysis, 2013
We establish theorems of strong convergence, for the Ishikawa-type (or two step; cf. Ishikawa, 1974) iteration scheme, to a fixed point of a uniformly L-Lipschitzian asymptotically demicontractive mapping and a uniformly L-Lipschitzian hemicontractive ...
Kyung Soo Kim
doaj   +1 more source

Sublinearly Morse Boundary I: CAT(0) Spaces

, 2019
To every Gromov hyperbolic space X one can associate a space at infinity called the Gromov boundary of X. Gromov showed that quasi-isometries of hyperbolic metric spaces induce homeomorphisms on their boundaries, thus giving rise to a well-defined notion of the boundary of a hyperbolic group.
Qing, Yulan, Rafi, Kasra, Tiozzo, Giulio
openaire   +2 more sources

Invitation to Alexandrov geometry: CAT[0] spaces

, 2017
98 pages, 36 ...
Alexander, Stephanie, Kapovitch, Vitali, Petrunin, Anton   +2 more
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Rank-one isometries of proper CAT(0)-spaces [PDF]

, 2008
Ursula Hamenstaedt
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Rank Rigidity for CAT(0) spaces without 3-flats [PDF]

, 2022
Stephan Stadler
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CAT(0) spaces on which a certain type of singularity is bounded [PDF]

, 2010
Tetsu Toyoda
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