Faculty Advisor

Capogna, Luca

Abstract

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.

Publisher

Worcester Polytechnic Institute

Date Accepted

April 2017

Major

Mathematical Sciences

Project Type

Major Qualifying Project

Accessibility

Unrestricted

Advisor Department

Mathematical Sciences

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