The Dirichlet Problem in Hyperbolic Space

2013 ◽  
pp. 219-234
Author(s):  
Rafael López
Keyword(s):  
Dirichlet Problem ◽  
Hyperbolic Space

scholarly journals Gradient estimates for the constant mean curvature equation in hyperbolic space

2019 ◽  
Vol 150 (6) ◽  
pp. 3216-3230
Author(s):  
Rafael López
Keyword(s):  
Dirichlet Problem ◽  
Hyperbolic Space ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Gradient Estimates ◽  
Maximum Principles ◽  
Convex Domains ◽  
Curvature Equation ◽  
Mean Curvature Equation ◽  
The Mean

AbstractWe establish gradient estimates for solutions to the Dirichlet problem for the constant mean curvature equation in hyperbolic space. We obtain these estimates on bounded strictly convex domains by using the maximum principles theory of Φ-functions of Payne and Philippin. These estimates are then employed to solve the Dirichlet problem when the mean curvature H satisfies H < 1 under suitable boundary conditions.

Distance Distribution between Complex Network Nodes in Hyperbolic Space

2016 ◽  
Vol 25 (3) ◽  
pp. 223-236 ◽  
Author(s):  
Gregorio Alanis-Lobato ◽  
Miguel A. Andrade-Navarro ◽  
Keyword(s):  
Complex Network ◽  
Hyperbolic Space ◽  
Distance Distribution ◽  
Network Nodes

Solvability of one nonlocal Dirichlet problem for the Poisson equation

2019 ◽  
Vol 50 (1) ◽  
pp. 67-88
Author(s):  
Batirkhan Turmetov ◽  
Valery Karachik
Keyword(s):  
Dirichlet Problem ◽  
Poisson Equation ◽  
The Poisson Equation

Density of tube packings in hyperbolic space

2004 ◽  
Vol 214 (1) ◽  
pp. 127-145 ◽  
Author(s):  
Andrew Przeworski
Keyword(s):  
Hyperbolic Space

Convergence theorems for total asymptotically nonexpansive single-valued and quasi nonexpansive multi-valued mappings in hyperbolic spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Preeyalak Chuadchawna ◽  
Ali Farajzadeh ◽  
Anchalee Kaewcharoen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Hyperbolic Space ◽  
Hyperbolic Spaces ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive ◽  
Uniformly Convex Hyperbolic Space

Abstract In this paper, we discuss the Δ-convergence and strong convergence for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a total asymptotically nonexpansive single-valued mapping and a quasi nonexpansive multi-valued mapping in a complete uniformly convex hyperbolic space. Finally, by giving an example, we illustrate our result.

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