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# A nonlinear partial differential equation for the volume preserving mean curvature flow

@article{Antonopoulou2013ANP, title={A nonlinear partial differential equation for the volume preserving mean curvature flow}, author={D. C. Antonopoulou and Georgia D. Karali}, journal={NHM}, year={2013}, volume={8}, pages={9-22} }

- Published 2013 in NHM
DOI:10.3934/nhm.2013.8.9

We analyze the evolution of multi-dimensional normal graphs over the unit sphere under volume preserving mean curvature flow and derive a non-linear partial differential equation in polar coordinates. Furthermore, we construct finite difference numerical schemes and present numerical results for the evolution of non-convex closed plane curves under this flow, to observe that they become convex very fast.