scholarly journals On the nature of isolated asymptotic singularities of solutions of a family of quasi-linear elliptic PDE's on a Cartan–Hadamard manifold

2019 ◽  
Vol 27 (4) ◽  
pp. 791-807 ◽  
Author(s):  
Leonardo Bonorino ◽  
Jaime Ripoll
Keyword(s):  
Hadamard Manifold

Generalized Fermat's Problem

1991 ◽  
Vol 34 (1) ◽  
pp. 96-104 ◽  
Author(s):  
R. Noda ◽  
T. Sakai ◽  
M. Morimoto
Keyword(s):  
Hadamard Manifold ◽  
The Given

AbstractThe following problem is studied. Generalized Fermat's problem: in an n-dimensional Hadamard manifold M, locate a point whose distances from the given k vertices of M have the smallest possible sum.

ON RICCI RANK OF CARTAN–HADAMARD MANIFOLDS

2002 ◽  
Vol 13 (06) ◽  
pp. 557-578
Author(s):  
DINCER GULER ◽  
FANGYANG ZHENG
Keyword(s):  
Lower Bound ◽  
Ricci Tensor ◽  
Hadamard Manifold ◽  
Hadamard Manifolds ◽  
The Core ◽  
Maximum Rank

In this article, we prove that the maximum rank r of the Ricci tensor of a Cartan–Hadamard manifold Mn satisfies the inequality 2r - 1 ≥ n - s, where n is the dimension and s is the core number, which measures the flatness of Mn. Examples show that this lower bound is sharp.

scholarly journals On the Asymptotic Dirichlet Problem for the Minimal Hypersurface Equation in a Hadamard Manifold

2017 ◽  
Vol 47 (4) ◽  
pp. 485-501 ◽  
Author(s):  
Jean-Baptiste Casteras ◽  
Ilkka Holopainen ◽  
Jaime B. Ripoll
Keyword(s):  
Dirichlet Problem ◽  
Minimal Hypersurface ◽  
Hadamard Manifold

scholarly journals A NOTE ON THE UNCLOUDING THE SKY OF NEGATIVELY CURVED MANIFOLDS

2008 ◽  
Vol 77 (3) ◽  
pp. 413-424
Author(s):  
ALBERT BORBÉLY
Keyword(s):  
Convex Sets ◽  
Hadamard Manifold ◽  
Curved Manifolds ◽  
Negatively Curved ◽  
Arbitrary Convex

AbstractThe problem of finding geodesics that avoid certain obstacles in negatively curved manifolds has been studied in different situations. In this note we give a generalization of the unclouding theorem of J. Parkkonen and F. Paulin: there is a constant s0=1.534 such that for any Hadamard manifold M with curvature ≤−1 and for any family of disjoint balls or horoballs {Ca}a∈A and for any point p∈M−⋃ a∈ACa if we shrink these balls uniformly by s0 one can always find a geodesic ray emanating from p that avoids the shrunk balls. It will be shown that in the theorem above one can replace the balls by arbitrary convex sets.

Information geometry of Busemann-barycenter for probability measures

2015 ◽  
Vol 26 (06) ◽  
pp. 1541007 ◽  
Author(s):  
Mitsuhiro Itoh ◽  
Hiroyasu Satoh
Keyword(s):  
Natural Extension ◽  
Information Geometry ◽  
Acta Math ◽  
Space Structure ◽  
Hadamard Manifold ◽  
Probability Measures ◽  
Positive Density ◽  
Ideal Boundary ◽  
Push Forward ◽  
The Ideal

Using Busemann function of an Hadamard manifold X we define the barycenter map from the space 𝒫+(∂X, dθ) of probability measures having positive density on the ideal boundary ∂X to X. The space 𝒫+(∂X, dθ) admits geometrically a fiber space structure over X from Fisher information geometry. Following the arguments in [E. Douady and C. Earle, Conformally natural extension of homeomorphisms of the circle, Acta Math.157 (1986) 23–48; G. Besson, G. Courtois and S. Gallot, Entropies et rigidités des espaces localement symétriques de coubure strictement négative, Geom. Funct. Anal.5 (1995) 731–799; Minimal entropy and Mostow's rigidity theorems, Ergodic Theory Dynam. Systems16 (1996) 623–649], we exhibit that under certain geometrical hypotheses a homeomorphism Φ of the ideal boundary ∂X induces, by the aid of push-forward, an isometry of X whose extension is Φ.

scholarly journals Nonsolvability of the asymptotic Dirichlet problem for the p-Laplacian on Cartan–Hadamard manifolds

2016 ◽  
Vol 9 (2) ◽  
Author(s):  
Ilkka Holopainen
Keyword(s):  
Dirichlet Problem ◽  
Hadamard Manifold ◽  
Hadamard Manifolds ◽  
3 Dimensional

AbstractWe construct, by modifying Borbély's example, a 3-dimensional Cartan–Hadamard manifold

scholarly journals Solving Yosida inclusion problem in Hadamard manifold

2019 ◽  
Vol 9 (2) ◽  
pp. 357-366 ◽  
Author(s):  
Mohammad Dilshad
Keyword(s):  
Approximate Solution ◽  
Vector Field ◽  
Variational Inequalities ◽  
Hadamard Manifold ◽  
Inclusion Problem ◽  
Approximation Operator ◽  
Hadamard Manifolds ◽  
Yosida Approximation ◽  
Type Algorithm ◽  
Monotone Vector Field

Abstract We consider a Yosida inclusion problem in the setting of Hadamard manifolds. We study Korpelevich-type algorithm for computing the approximate solution of Yosida inclusion problem. The resolvent and Yosida approximation operator of a monotone vector field and their properties are used to prove that the sequence generated by the proposed algorithm converges to the solution of Yosida inclusion problem. An application to our problem and algorithm is presented to solve variational inequalities in Hadamard manifolds.

scholarly journals Explicit Iterative Method for Variational Inequalities on Hadamard Manifolds

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Iterative Method ◽  
Variational Inequalities ◽  
New Method ◽  
Hadamard Manifold ◽  
Hadamard Manifolds ◽  
Auxiliary Principle ◽  
Auxiliary Principle Technique ◽  
Monotonicity Results

An explicit iterative method for solving the variational inequalities on Hadamard manifold is suggested and analyzed using the auxiliary principle technique. The convergence of this new method requires only the partially relaxed strongly monotonicity, which is a weaker condition than monotonicity. Results can be viewed as refinement and improvement of previously known results.

Sign in / Sign up

Export Citation Format

Share Document