Location of the weighted Fermat–Torricelli point on the K-plane
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Anastasios N. Zachos
Summary
We obtain the equations that allow us to compute the position of the weighted Fermat-Torricelli point on the two dimensional sphere SK2 of constant Gaussian curvature K and on the two dimensional hyperbolic plane HK2 of constant Gaussian curvature K for K <0; by introducing a method of symmetrical differentiation of a length of a geodesic arc with respect to two variable lengths of geodesic arcs, respectively. The method of differentiating a length of a geodesic arc with respect to two variable lengths of geodesic arcs is a generalization of the first variation formula of the length of a geodesic arc with respect to one variable length of geodesic arc on the K-plane.
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Articles in the same Issue
- Remarks on L2 boundedness of Littlewood–Paley operators
- A note on regularity for then-dimensional H-system assuming logarithmic higher integrability
- Convergence, monotonicity, and inequalities of sequences involving continued powers
- Location of the weighted Fermat–Torricelli point on the K-plane
- Zweier I-convergent sequence spaces defined by Orlicz function
- Solution of the Dirichlet problem for G-minimal graphs with a continuity and approximation method
- Tight wavelet frames on local fields
Articles in the same Issue
- Remarks on L2 boundedness of Littlewood–Paley operators
- A note on regularity for then-dimensional H-system assuming logarithmic higher integrability
- Convergence, monotonicity, and inequalities of sequences involving continued powers
- Location of the weighted Fermat–Torricelli point on the K-plane
- Zweier I-convergent sequence spaces defined by Orlicz function
- Solution of the Dirichlet problem for G-minimal graphs with a continuity and approximation method
- Tight wavelet frames on local fields
