scholarly journals A characterization of convex hypersurfaces in Hadamard manifolds

2005 ◽  
Vol 97 (1) ◽  
pp. 40
Author(s):  
Mehmet Erdogan ◽  
Gülsen Yilmaz
Keyword(s):  
Hadamard Manifold ◽  
Hadamard Manifolds ◽  
Strictly Convex ◽  
Convex Hypersurfaces

The aim of this paper is to give a characterization of strictly convex hypersurfaces in a Hadamard manifold.

STATIONARY DISCS AND GEOMETRY OF CR MANIFOLDS OF CODIMENSION TWO

2001 ◽  
Vol 12 (08) ◽  
pp. 877-890 ◽  
Author(s):  
A. SUKHOV ◽  
A. TUMANOV
Keyword(s):  
Contact Structure ◽  
Cr Manifolds ◽  
Codimension Two ◽  
Strictly Convex ◽  
Cr Structure ◽  
Conormal Bundle ◽  
Convex Hypersurfaces

We give a construction of stationary discs and the indicatrix for manifolds of higher codimension which is a partial analog of L. Lempert's theory of stationary discs for strictly convex hypersurfaces. This leads to new invariants of the CR structure in higher codimension linked with the contact structure of the conormal bundle.

Prescribing Centro-Affine Curvature From One Convex Body to Another

2020 ◽  
Author(s):  
Alina Stancu
Keyword(s):  
Convex Body ◽  
Convex Bodies ◽  
Minkowski Inequality ◽  
Curvature Flow ◽  
Constant Volume ◽  
Convex Hypersurface ◽  
Strictly Convex ◽  
Initial Hypersurface ◽  
Affine Curvature ◽  
Convex Hypersurfaces

Abstract We study a curvature flow on smooth, closed, strictly convex hypersurfaces in $\mathbb{R}^n$, which commutes with the action of $SL(n)$. The flow shrinks the initial hypersurface to a point that, if rescaled to enclose a domain of constant volume, is a smooth, closed, strictly convex hypersurface in $\mathbb{R}^n$ with centro-affine curvature proportional, but not always equal, to the centro-affine curvature of a fixed hypersurface. We outline some consequences of this result for the geometry of convex bodies and the logarithmic Minkowski inequality.

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 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 Self-similar solutions to fully nonlinear curvature flows by high powers of curvature

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Shanze Gao ◽  
Haizhong Li ◽  
Xianfeng Wang
Keyword(s):  
Large Family ◽  
Concave Function ◽  
Principal Curvatures ◽  
Fully Nonlinear ◽  
Strictly Convex ◽  
Self Similar ◽  
Speed Function ◽  
Similar Solutions ◽  
Convex Hypersurfaces

Abstract In this paper, we investigate closed strictly convex hypersurfaces in ℝ n + 1 {\mathbb{R}^{n+1}} which shrink self-similarly under a large family of fully nonlinear curvature flows by high powers of curvature. When the speed function is given by powers of a homogeneous of degree 1 and inverse concave function of the principal curvatures with power greater than 1, we prove that the only such hypersurfaces are round spheres. We also prove that slices are the only closed strictly convex self-similar solutions to such curvature flows in the hemisphere 𝕊 + n + 1 {\mathbb{S}^{n+1}_{+}} with power greater than or equal to 1.

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.

A CHARACTERIZATION OF STRICTLY CONVEX LINEAR 2-NOBMED SPACES

1989 ◽  
Vol 12 (2) ◽  
pp. 201-204
Author(s):  
Sizwe Mabizela
Keyword(s):  
Strictly Convex
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