Can Mean-Curvature Flow be Modified to be Non-singular?

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Date
2012
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and Blackwell Publishing Ltd.
Abstract
This work considers the question of whether mean-curvature flow can be modified to avoid the formation of singularities. We analyze the finite-elements discretization and demonstrate why the original flow can result in numerical instability due to division by zero. We propose a variation on the flow that removes the numerical instability in the discretization and show that this modification results in a simpler expression for both the discretized and continuous formulations. We discuss the properties of the modified flow and present empirical evidence that not only does it define a stable surface evolution for genus-zero surfaces, but that the evolution converges to a conformal parameterization of the surface onto the sphere.
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@article{
10.1111:j.1467-8659.2012.03179.x
, journal = {Computer Graphics Forum}, title = {{
Can Mean-Curvature Flow be Modified to be Non-singular?
}}, author = {
Kazhdan, Michael
and
Solomon, Jake
and
Ben-Chen, Mirela
}, year = {
2012
}, publisher = {
The Eurographics Association and Blackwell Publishing Ltd.
}, ISSN = {
1467-8659
}, DOI = {
10.1111/j.1467-8659.2012.03179.x
} }
Citation