• Title/Summary/Keyword: Hadamard-Cartan theorem

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CONVEXITY OF DISTANCE FUNCTION BETWEEN GEODESICS

  • Kim, In-Su;Kim, Yong-Il;Lee, Doo-Hann
    • Honam Mathematical Journal
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    • v.30 no.2
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    • pp.335-341
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    • 2008
  • In this paper, we use the convexity of distance function between geodesics in a singular Hadamard space to generalize Hadamard-Cartan theorem for 2-dimensional metric spaces. We also determine a neighborhood of a closed geodesic where no other closed geodesic exists in a complete space of nonpositive curvature.

JORDAN AUTOMORPHIC GENERATORS OF EUCLIDEAN JORDAN ALGEBRAS

  • Kim, Jung-Hwa;Lim, Yong-Do
    • Journal of the Korean Mathematical Society
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    • v.43 no.3
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    • pp.507-528
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    • 2006
  • In this paper we show that the Koecher's Jordan automorphic generators of one variable on an irreducible symmetric cone are enough to determine the elements of scalar multiple of the Jordan identity on the attached simple Euclidean Jordan algebra. Its various geometric, Jordan and Lie theoretic interpretations associated to the Cartan-Hadamard metric and Cartan decomposition of the linear automorphisms group of a symmetric cone are given with validity on infinite-dimensional spin factors

Stability and Constant Boundary-Value Problems of f-Harmonic Maps with Potential

  • Kacimi, Bouazza;Cherif, Ahmed Mohammed
    • Kyungpook Mathematical Journal
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    • v.58 no.3
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    • pp.559-571
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    • 2018
  • In this paper, we give some results on the stability of f-harmonic maps with potential from or into spheres and any Riemannian manifold. We study the constant boundary-value problems of such maps defined on a specific Cartan-Hadamard manifolds, and obtain a Liouville-type theorem. It can also be applied to the static Landau-Lifshitz equations. We also prove a Liouville theorem for f-harmonic maps with finite f-energy or slowly divergent f-energy.

ASYMPTOTIC BEHAVIOR OF HARMONIC MAPS AND EXPONENTIALLY HARMONIC FUNCTIONS

  • Chi, Dong-Pyo;Choi, Gun-Don;Chang, Jeong-Wook
    • Journal of the Korean Mathematical Society
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    • v.39 no.5
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    • pp.731-743
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    • 2002
  • Let M be a Riemannian manifold with asymptotically non-negative curvature. We study the asymptotic behavior of the energy densities of a harmonic map and an exponentially harmonic function on M. We prove that the energy density of a bounded harmonic map vanishes at infinity when the target is a Cartan-Hadamard manifold. Also we prove that the energy density of a bounded exponentially harmonic function vanishes at infinity.