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Branching geodesics in normed spaces
Izvestiya: Mathematics, 2002Summary: We study branching extremals of length functionals on normed spaces. This is a natural generalization of the Steiner problem in normed spaces. We obtain criteria for a network to be extremal under deformations that preserve the topology of networks as well as under deformations with splitting. We discuss the connection between locally shortest
Ivanov, A. O., Tuzhilin, A. A.
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On Geodesics in Euclidean Shape Spaces
Journal of the London Mathematical Society, 1991The geometry of the shape spaces \(\Sigma_ m^ k\) has been developed in [\textit{D. G. Kendall}, Bull. Lond. Math. Soc. 16, 81-121 (1984; Zbl 0579.62100); \textit{T.K. Carne}, Proc. Lond. Math. Soc., III. Ser. 61, No. 2, 407-432 (1990; Zbl 0723.60014)] and in a recent joint paper of the author and D. Kendall.
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The Monge Problem in Geodesic Spaces
2011We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish non branching geodesic space. We show that we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce an assumption on the transport problem π which implies that the conditional probabilities of the first marginal on ...
S. Bianchini, F. Cavalletti
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On a Class of Geodesics in Teichmuller Space
The Annals of Mathematics, 1975The study of the geometry of the classical Teichmiiller spaces was begun in 1959 by Kravetz [9]. The starting point was the classical theorem of TeichmUller on extremal quasiconformal maps between compact Riemann surfaces. The TeichmUller theorem was used to argue that with respect to the Teichmiiller metric, TeichmUller space is straight and that it ...
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Generalised geodesics in a Riemannian space
Bulletin de la Classe des sciences, 1967Asymptotic lines of order p have been defined by Hayden in [1]. In this paper we define geodesies of order p, investigate their properties and establish their relationship with the asymptotic lines of order p.
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Journal of Geometry and Physics, 1993
The space of smooth embedded loops \(E(S^ 1,M) \subset C^ \infty(S^ 1,M)\) in a Riemannian manifold \((M,g)\) carries a (weak) Riemannian metric \[ G(\gamma)(s_ 1,s_ 2) = \int_{S^ 1} g(s_ 1(t),s_ 2(t))\text{vol}(\gamma^* g)(t), \] where \(s_ i \in T_ \gamma C^ \infty(S^ 1,M)\) `is' the space of all vector fields along \(\gamma\), which is invariant ...
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The space of smooth embedded loops \(E(S^ 1,M) \subset C^ \infty(S^ 1,M)\) in a Riemannian manifold \((M,g)\) carries a (weak) Riemannian metric \[ G(\gamma)(s_ 1,s_ 2) = \int_{S^ 1} g(s_ 1(t),s_ 2(t))\text{vol}(\gamma^* g)(t), \] where \(s_ i \in T_ \gamma C^ \infty(S^ 1,M)\) `is' the space of all vector fields along \(\gamma\), which is invariant ...
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On the Electromagnetic Geodesic in Space
We present a field-theoretic framework for modeling electromagnetic energy propagation in heterogeneous media by introducing the concept of electromagnetic geodesics. Unlike traditional ray optics, which assumes either a straight-line propagation or a simple bending in refractive media, our approach formulates wave propagation as geodetic motion in a ...Jacob T Fokkema, Peter M van den berg
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Geodesic PCA in the Wasserstein space by convex PCA
Annales De L'institut Henri Poincare (B) Probability and Statistics, 2017Jeremie Bigot, Thierry Klein
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Geodesic connectedness in Gödel type space-times
Differential Geometry and Its Applications, 2000Anna Maria Candela
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