scholarly journals Existence and uniqueness of minimal graphs in hyperbolic space

2000 ◽  
Vol 4 (3) ◽  
pp. 669-694 ◽  
Author(s):  
Ricardo Sa Earp ◽  
Eric Toubiana
Keyword(s):  
Hyperbolic Space ◽  
Existence And Uniqueness ◽  
Minimal Graphs

scholarly journals Horosphere slab separation theorems in manifolds without conjugate points

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Sameh Shenawy
Keyword(s):  
Euclidean Space ◽  
Hyperbolic Space ◽  
Existence And Uniqueness ◽  
Convex Set ◽  
Sufficient Conditions ◽  
Conjugate Points ◽  
Separation Theorems ◽  
Farthest Points ◽  
Simply Connected ◽  
Convex Subsets

Abstract Let $\mathcal {W}^{n}$ W n be the set of smooth complete simply connected n-dimensional manifolds without conjugate points. The Euclidean space and the hyperbolic space are examples of these manifolds. Let $W\in \mathcal {W}^{n}$ W ∈ W n and let A and B be two convex subsets of W. This note aims to investigate separation and slab horosphere separation of A and B. For example,sufficient conditions on A and B to be separated by a slab of horospheres are obtained. Existence and uniqueness of foot points and farthest points of a convex set A in $W\in \mathcal {W}$ W ∈ W are considered.

scholarly journals Existence and uniqueness of singular solutions for elliptic equation on the hyperbolic space

2013 ◽  
Vol 13 (2) ◽  
pp. 949-960 ◽  
Author(s):  
Yen-Lin Wu ◽  
Zhi-You Chen ◽  
Jann-Long Chern ◽  
Y. Kabeya
Keyword(s):  
Elliptic Equation ◽  
Hyperbolic Space ◽  
Existence And Uniqueness ◽  
Singular Solutions

scholarly journals Refined asymptotics for minimal graphs in the hyperbolic space

2017 ◽  
Vol 62 (2) ◽  
pp. 381-390 ◽  
Author(s):  
Weiming Shen ◽  
Yue Wang
Keyword(s):  
Hyperbolic Space ◽  
Minimal Graphs

scholarly journals On nonlocal minimal graphs

2021 ◽  
Vol 60 (4) ◽  
Author(s):  
Matteo Cozzi ◽  
Luca Lombardini
Keyword(s):  
Existence And Uniqueness ◽  
A Priori Estimates ◽  
A Priori ◽  
Analytic Approach ◽  
Comparison Principles ◽  
Minimal Graphs ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Priori Estimates ◽  
Rearrangement Inequalities

AbstractWe develop a functional analytic approach for the study of nonlocal minimal graphs. Through this, we establish existence and uniqueness results, a priori estimates, comparison principles, rearrangement inequalities, and the equivalence of several notions of minimizers and solutions.

Sign in / Sign up

Export Citation Format

Share Document