CEU Electronic Theses and Dissertations, 2010
| Author | Kristaly, Alexandru |
|---|---|
| Title | Economic Optimization Problems via Riemann-Finsler Geometry |
| Summary | The purpose of the present thesis is to study economic optimization problems within a non-linear, geometrical framework, motivated by various examples occuring in our daily life. In order to describe and explain such phenomena, we exploit elements from Riemann-Finsler geometry. In the first chapter we recall notions and results from Riemann-Finsler geometry which will be used in the thesis. We also present new material on Busemann NPC spaces on Finsler manifolds which solves partially a fifty-year-old open problem of Busemann and Pedersen. In the second chapter we study a general Weber location problem with unit weights on Finsler manifolds, i.e., to minimize the sum of distances (the cost of transportation) to the sample points situated on a not necessarily reversible Finsler manifold. Some existence, uniqueness and multiplicity results are presented in various geometrical contexts together with some practical examples. In the third chapter existence and location of Nash-type equilibrium points are studied for a large class of finite families of payoff functions whose domains are not necessarily convex in the usual sense. The geometric idea is to embed these non-convex domains into suitable Riemannian manifolds, thus regaining certain geodesic convexity properties of them. By using variational inequalities, set-valued analysis, dynamical systems, and non-smooth calculus on Riemannian manifolds, various existence, location and stability results of Nash-type equilibrium points are derived. Some of the results can be obtained only on Hadamard manifolds as a curvature rigidity result shows. |
| Supervisor | Gheorghe Morosanu |
| Department | Mathematics PhD |
| Full text | https://www.etd.ceu.edu/2010/kristaly_alexandru.pdf |
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