The Mann algorithm in a complete geodesic space with curvature bounded above

Halpern iteration for strongly quasinonexpansive mappings on a geodesic space with curvature bounded above by one

*Correspondence: [email protected] 1Department of Information Science, Toho University, Miyama, Funabashi, Chiba 274-8510, Japan Full list of author information is available at the end of the article Abstract In this paper, we deal with the Halpern iterative scheme for a strongly quasinonexpansive mapping in the setting of a complete geodesic space with curvature bounded above by one...

The local structure of length spaces with curvature bounded above

We show that a number of different notions of dimension coincide for length spaces with curvature bounded above. We then apply this result, showing that if X is a locally compact CAT (0) space with cocompact isometry group, then the dimension of the Tits boundary and the asymptotic cone(s) of X are determined by the maximal dimension of a flat in X .

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Measuring Geodesic Distances on the Space of Bounded Diffeomorphisms

This paper considers the problem of measuring the differences between deformations. It is intended to be applied in the context of applications such as the analysis of sets of non-rigidly registered medical images, where diffeomorphic warps between pairs of images establish a dense pixel-to-pixel correspondence. We introduce a new spline with explicit boundary conditions, and show how this can ...

Total Curvature and Simple Pursuit on Domains of Curvature Bounded Above

We show how circumradius and asymptotic behavior of curves in CAT(0) and CAT(K) spaces (K > 0) are controlled by growth rates of total curvature. We apply our results to pursuit and evasion games of capture type with simple pursuit motion, generalizing results that are known for convex Euclidean domains, and obtaining results that are new for convex Euclidean domains and hold on playing fields ...