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
Enclosure and non-existence theorems for area stationary currents and currents with mean curvature vector
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DOI: 10.1007/s00013-020-01461-4
Abstract: We discuss certain geometric properties for area stationary currents and currents with integrable mean curvature, so called “enclosure theorems”. As a consequence, we obtain non-existence results for currents with connected support. Finally, we extend these… read more here.
Keywords: mean curvature; stationary currents; currents currents; area stationary ... 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
A new functional for the Calculus of Variations, involving the variational mean curvature of sets in $$R^n$$Rn
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DOI: 10.1007/s00229-017-0985-9
Abstract: We study the pth power $$W_p(E)=\int _{{\mathbb R}^n}|H_E|^p\,dx$$Wp(E)=∫Rn|HE|pdx, where $$H_E$$HE is the variational mean curvature of E, as defined in Barozzi (Rend Mat Acc Linceis 9(5):149–159, 1994) (see also in Proc Am Math Soc 99:313–316,… read more here.
Keywords: variational mean; mean curvature; functional calculus; new functional ... See more keywords
On semidiscrete constant mean curvature surfaces and their associated families
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DOI: 10.1007/s00605-016-0929-6
Abstract: The present paper studies semidiscrete surfaces in three-dimensional Euclidean space within the framework of integrable systems. In particular, we investigate semidiscrete surfaces with constant mean curvature along with their associated families. The notion of mean… read more here.
Keywords: associated families; mean curvature; semidiscrete surfaces; constant mean ... See more keywords
Heinz mean curvature estimates in warped product spaces $$M\times _{e^{\psi }}N$$M×eψN
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DOI: 10.1007/s10455-017-9577-x
Abstract: If a graph submanifold (x, f(x)) of a Riemannian warped product space $$(M^m\times _{e^{\psi }}N^n,\tilde{g}=g+ e^{2\psi }h)$$(Mm×eψNn,g~=g+e2ψh) is immersed with parallel mean curvature H, then we obtain a Heinz-type estimation of the mean curvature. Namely, on… read more here.
Keywords: warped product; psi; mean curvature; times psi ... See more keywords
The r-mean curvature and rigidity of compact hypersurfaces in the Euclidean space
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DOI: 10.1007/s10455-021-09803-3
Abstract: In this paper, we characterize round spheres in the Euclidean space under some suitable conditions on the r-mean curvature. read more here.
Keywords: curvature rigidity; mean curvature; euclidean space; rigidity compact ... 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
Image Segmentation via Mean Curvature Regularized Mumford-Shah Model and Thresholding
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DOI: 10.1007/s11063-017-9763-7
Abstract: Due to the limitations in imaging devices and subject-induced susceptibility effect, general image segmentation is still an open problem. Typical challenges include image noise, intensity inhomogeneity and various image modalities. In this paper, we propose… read more here.
Keywords: mean curvature; image; segmentation; image segmentation ... See more keywords