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.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Shen, Weizhe

Publisher

• Worcester Polytechnic Institute

Identifier

• E-project-042517-194836

Advisor

• Capogna, Luca

Year

• 2017

Date created

• 2017-04-25

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences

Rights statement

• In Copyright