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Conformalized Mean Curvature Flow

Student-Run Applied & Math Seminar

Speaker: Ka Wai Wong, UC Davis
Related Webpage: https://www.math.ucdavis.edu/~wong0925/
Location: 2112 MSB
Start time: Thu, May 3 2018, 12:10PM

My ultimate goal is to compare any two different compact genus-zero surfaces. One idea proposed by Joel Hass and Patrice Koehl is to have a conformal map that constructs a notion of distance, a "metric", between two surfaces in the space of shapes. This conformal map is chosen to minimize certain energy functional measuring area distortion between the two surfaces. The difficulty in computing this metric lies in finding a discrete conformal mapping algorithm to map the surface onto a round unit sphere. A paper "Can Mean-Curvature Flow Be Made Non-Singular?" by Kazhdan, Solomon, and Ben-Chen suggested that such a discrete conformal can be obtained by a modified version of mean curvature flow. My talk will mainly focus on their results. A few fun animations will be shown during the talk.

As a teaser and possible application of this research, please take a look at the video kindly provided by Prof. Keenan Crane on "Robust fairing via Conformal Curvature Flow": https://www.youtube.com/watch?v=Jhqlmcms04M



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