The objective of this project was to quantify the difference between two planar domains with finitely prescribed matching points. To this end, we use gradient flows to obtain a homotopy of quasiconformal mappings between the two shapes, find a canonical minimizer for maximal infinitesimal stretching and rotation, and take the distortion of the minimizer as a measure of the difference between the two planar shapes. In our approach, numerical implementation is applied to get better insight of the long-time behavior of the gradient flow.
Worcester Polytechnic Institute
Major Qualifying Project
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