Results 21 to 30 of about 654,693 (352)
Pinched hypersurfaces are compact
Advanced Nonlinear Studies, 2023 We make rigorous and old idea of using mean curvature flow to prove a theorem of Richard Hamilton on the compactness of proper hypersurfaces with pinched, bounded curvature.
Bourni Theodora +2 more
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Nonlocal diffusion of smooth sets
Mathematics in Engineering, 2022 We consider normal velocity of smooth sets evolving by the $ s- $fractional diffusion. We prove that for small time, the normal velocity of such sets is nearly proportional to the mean curvature of the boundary of the initial set for $ s\in [\frac{1}{2},
Anoumou Attiogbe +2 more
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The fractional mean curvature flow
Bruno Pini Mathematical Analysis Seminar, 2020 In this note, we present some recent results in the study of the fractional mean curvature flow, that is a geometric evolution of the boundary of a set whose speed is given by the fractional mean curvature.
Eleonora Cinti
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Non-Parametric Mean Curvature Flow with Prescribed Contact Angle in Riemannian Products
Analysis and Geometry in Metric Spaces, 2022 Assuming that there exists a translating soliton u∞ with speed C in a domain Ω and with prescribed contact angle on ∂Ω, we prove that a graphical solution to the mean curvature flow with the same prescribed contact angle converges to u∞ + Ct as t →∞.
Casteras Jean-Baptiste +3 more
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Convergence Rates of the Allen-Cahn Equation to Mean Curvature Flow: A Short Proof Based on Relative Entropies [PDF]
SIAM Journal on Mathematical Analysis, 2020 We give a short and self-contained proof for rates of convergence of the Allen-Cahn equation towards mean curvature flow, assuming that a classical (smooth) solution to the latter exists and starting from well-prepared initial data. Our approach is based
J. Fischer, Tim Laux, Thilo M. Simon
semanticscholar +1 more source
The local structure of the energy landscape in multiphase mean curvature flow: Weak-strong uniqueness and stability of evolutions [PDF]
Journal of the European Mathematical Society (Print), 2020 We prove that in the absence of topological changes, the notion of \operatorname{BV} solutions to planar multiphase mean curvature flow does not allow for a mechanism for (unphysical) non-uniqueness.
J. Fischer +3 more
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Mean curvature flow with surgery [PDF]
Duke Mathematical Journal, 2017 We give a new proof for the existence of mean curvature flow with surgery of 2-convex hypersurfaces in $R^N$, as announced in arXiv:1304.0926. Our proof works for all $N \geq 3$, including mean convex surfaces in $R^3$. We also derive a priori estimates for a more general class of flows in a local and flexible setting.
Haslhofer, Robert, Kleiner, Bruce
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Quantitative Alexandrov theorem and asymptotic behavior of the volume preserving mean curvature flow [PDF]
Analysis & PDE, 2020 We prove a new quantitative version of the Alexandrov theorem which states that if the mean curvature of a regular set in R^{n+1} is close to a constant in L^{n}-sense, then the set is close to a union of disjoint balls with respect to the Hausdorff ...
Vesa Julin, J. Niinikoski
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Recent rigidity results for graphs with prescribed mean curvature
Mathematics in Engineering, 2021 This survey describes some recent rigidity results obtained by the authors for the prescribed mean curvature problem on graphs u : M → R. Emphasis is put on minimal, CMC and capillary graphs, as well as on graphical solitons for the mean curvature flow ...
Bruno Bianchini +5 more
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Bulletin of the American Mathematical Society, 2015 Mean curvature flow is the negative gradient flow of volume, so any hypersurface flows through hypersurfaces in the direction of steepest descent for volume and eventually becomes extinct in finite time. Before it becomes extinct, topological changes can occur as it goes through singularities. If the hypersurface is in general or generic position, then
Colding, Tobias +2 more
openaire +2 more sources