scholarly journals Total Curvature and the Isoperimetric Inequality in Cartan–Hadamard Manifolds

2022 ◽  
Vol 32 (2) ◽  
Author(s):  
Mohammad Ghomi ◽  
Joel Spruck
Keyword(s):  
Isoperimetric Inequality ◽  
Total Curvature ◽  
Hadamard Manifolds

Harmonic p-forms on Hadamard manifolds with finite total curvature

2018 ◽  
Vol 54 (4) ◽  
pp. 473-487
Author(s):  
Peijun Wang ◽  
Xiaoli Chao ◽  
Yilong Wu ◽  
Yusha lv
Keyword(s):  
Total Curvature ◽  
Hadamard Manifolds ◽  
Finite Total Curvature

scholarly journals The ideal boundaries and global geometric properties of complete open surfaces

1990 ◽  
Vol 120 ◽  
pp. 181-204 ◽  
Author(s):  
Takashi Shioya
Keyword(s):  
Equivalence Relation ◽  
Focal Point ◽  
Asymptotic Relation ◽  
Total Curvature ◽  
Equivalence Classes ◽  
Hadamard Manifold ◽  
Hadamard Manifolds ◽  
Ideal Boundary ◽  
Geometric Properties ◽  
The Ideal

In this paper we study the ideal boundaries of surfaces admitting total curvature as a continuation of [Sy2] and [Sy3]. The ideal boundary of an Hadamard manifold is defined to be the equivalence classes of rays. This equivalence relation is the asymptotic relation of rays, defined by Busemann [Bu]. The asymptotic relation is not symmetric in general. However in Hadamard manifolds this becomes symmetric. Here it is essential that the manifolds are focal point free.

scholarly journals Common Solution for a Finite Family of Equilibrium Problems, Quasi-Variational Inclusion Problems and Fixed Points on Hadamard Manifolds

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1161
Author(s):  
Jinhua Zhu ◽  
Jinfang Tang ◽  
Shih-sen Chang ◽  
Min Liu ◽  
Liangcai Zhao
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Variational Inclusion ◽  
Point Problem ◽  
Hadamard Manifolds ◽  
Inclusion Problems ◽  
Common Solution

In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in literature.

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