Mean curvature flow with free boundary – Type 2 singularities
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DOI: 10.1002/mana.201800156
Abstract: In this paper we give sufficient conditions that guarantee the mean curvature flow with free boundary on a pinched cylinder develops a Type 2 curvature singularity. We additionally prove that Type 0 singularities may only… read more here.
Keywords: mean curvature; free boundary; type singularities; curvature flow ... See more keywords
Invariant solutions of the normal hyperbolic mean curvature flow with dissipation
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DOI: 10.1007/s00013-019-01397-4
Abstract: In this paper, based on the classical Lie symmetry method, the group invariant solutions of the normal hyperbolic mean curvature flow with dissipation are discussed. The optimal system of the obtained symmetries is found, the… read more here.
Keywords: mean curvature; normal hyperbolic; solutions normal; curvature flow ... See more keywords
Mean Curvature Flow in Null Hypersurfaces and the Detection of MOTS
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DOI: 10.1007/s00220-022-04326-9
Abstract: We study the mean curvature flow in 3-dimensional null hypersurfaces. In a spacetime a hypersurface is called null, if its induced metric is degenerate. The speed of the mean curvature flow of spacelike surfaces in… read more here.
Keywords: curvature; hypersurface; curvature flow; null hypersurfaces ... See more keywords
The extension problem of the mean curvature flow (I)
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DOI: 10.1007/s00222-019-00893-2
Abstract: AbstractWe show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow in $${{\mathbb {R}}}^3$$R3. read more here.
Keywords: mean curvature; curvature flow; extension problem; curvature ... See more keywords
The Effective Dynamics of the Volume Preserving Mean Curvature Flow
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DOI: 10.1007/s10955-018-2041-x
Abstract: We consider the dynamics of small closed submanifolds (‘bubbles’) under the volume preserving mean curvature flow. We construct a map from ($$\text {n}+1$$n+1)-dimensional Euclidean space into a given ($$\text {n}+1$$n+1)-dimensional Riemannian manifold which characterizes the… read more here.
Keywords: mean curvature; preserving mean; volume preserving; effective dynamics ... See more keywords
Free boundary regularity on the focusing problem for the Q curvature flow with flat sides I
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DOI: 10.1016/j.jfa.2020.108792
Abstract: Abstract In this paper, we consider the motion of a compact, weakly convex hypersurface of revolution Σ 0 ⊂ R n + 1 under the Q k curvature flow. Assume that Σ 0 has a… read more here.
Keywords: curvature flow; flow flat; flat side; side ... See more keywords
Harnack inequality and pinching estimates for anisotropic curvature flow of hypersurfaces
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2018.03.062
Abstract: Abstract We obtain a differential Harnack inequality for anisotropic curvature flow of convex hypersurfaces in Euclidean space with its speed given by a curvature function of homogeneity degree one in a certain class, and restrictions… read more here.
Keywords: harnack inequality; curvature flow; anisotropic curvature; curvature ... See more keywords
Global Regularity of Skew Mean Curvature Flow for Small Data in d ≥ 4 Dimensions
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DOI: 10.1093/imrn/rnad104
Abstract: The skew mean curvature flow is an evolution equation for a $d$ dimensional manifold immersed into $\mathbb {R}^{d+2}$, and which moves along the binormal direction with a speed proportional to its mean curvature. In this… read more here.
Keywords: skew mean; curvature flow; regularity; mean curvature ... See more keywords
Cylindrical estimates for mean curvature flow in hyperbolic spaces
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DOI: 10.3934/cpaa.2021016
Abstract: We consider the mean curvature flow of a closed hypersurface in hyperbolic space. Under a suitable pinching assumption on the initial data, we prove a priori estimate on the principal curvatures which implies that the… read more here.
Keywords: estimates mean; cylindrical estimates; curvature flow; mean curvature ... See more keywords