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- W4384157239 abstract "We investigate the formation of singularities for surfaces evolving by volume preserving mean curvature flow. For axially symmetric flows - surfaces of revolution - in $mathbb{R}^3$ with Neumann boundary conditions, we prove that the first developing singularity is of Type I. The result is obtained without any additional curvature assumptions being imposed, while axial symmetry and boundary conditions are justifiable given the volume constraint. Additional results and ingredients towards the main proof include a non-cylindrical parabolic maximum principle, and a series of estimates on geometric quantities involving gradient, curvature terms and derivatives thereof. These hold in arbitrary dimensions." @default.
- W4384157239 created "2023-07-14" @default.
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- W4384157239 date "2012-03-26" @default.
- W4384157239 modified "2023-09-24" @default.
- W4384157239 title "Singularities of Axially Symmetric Volume Preserving Mean Curvature Flow" @default.
- W4384157239 doi "https://doi.org/10.48550/arxiv.1203.5671" @default.
- W4384157239 hasPublicationYear "2012" @default.
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