Description
- Abstract:
- This thesis investigates three related topics on the geometry of the space of planarshapes.In the first part, we setup the EPDiff (Euler-Poincare equation on the group ofdiffeomorphisms) and investigate its singular solutions, Teichons, analogues of solitons.A symplectic integration scheme has been implemented to solve a Hamiltonianproblem that arises in this part.In the second part, the formula for the sectional curvature of the Weil-Peterssonmetric has been derived. It has been shown that the formula coincides with Arnold'sformula in the case of the metric without a null space.The third part concerns numerical implementation of optimization problem offinding geodesics by minimizing the Weil-Petersson energy. The comparison of methodsis shown alongside with the examples of geodesics.
- Notes:
- Thesis (Ph.D. -- Brown University (2010)
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Citation
Kushnarev, Sergey,
"The Geometry of the Space of 2D Shapes and theWeil-Petersson Metric"
(2010).
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z04T6GK8
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Applied Mathematics Theses and Dissertations
Theses and Dissertations for the Applied Mathematics department....