\(SO(2)\) symmetry of the translating solitons of the mean curvature flow in \(\mathbb{R}^4\) (Q2141667)
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scientific article; zbMATH DE number 7531774
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(SO(2)\) symmetry of the translating solitons of the mean curvature flow in \(\mathbb{R}^4\) |
scientific article; zbMATH DE number 7531774 |
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\(SO(2)\) symmetry of the translating solitons of the mean curvature flow in \(\mathbb{R}^4\) (English)
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25 May 2022
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Translating solitons are an important class of solutions to the mean curvature flow, which often arise as blow-up limit of type II singularities, following Hamilton's blow-up procedure. In this paper, the author proves that the translating solitons of the mean curvature flow in \(\mathbb R^4\) which arise as blow-up limit of embedded, mean convex mean curvature flow must have \(SO(2)\) symmetry, which means that they are invariant under \(SO(2)\) action.
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mean curvature flow
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soliton solution
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singularity analysis
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quasilinear parabolic PDE
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0.9351299
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0.9198712
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0.9185054
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0.91149247
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