Translators of the Mean Curvature Flow in Hyperbolic Einstein's Static Universe [PDF]
In this study, we deal with non-degenerate translators of the mean curvature flow in the well-known hyperbolic Einstein's static universe. We classify translators foliated by horospheres and rotationally invariant ones, both space-like and time-like. For
Ortega, Miguel, Yalçın, Buse
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A capillary problem for spacelike mean curvature flow in a cone of Minkowski space
, 2023 Consider a convex cone in three-dimensional Minkowski space which either contains the lightcone or is contained in it. This work considers mean curvature flow of a proper spacelike strictly mean convex disc in the cone which is graphical with respect to ...
Klingenberg, Wilhelm +2 more
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Discrete hyperbolic curvature flow in the plane
, 2022 Hyperbolic curvature flow is a geometric evolution equation that in the plane can be viewed as the natural hyperbolic analogue of curve shortening flow.
Deckelnick, Klaus, Nürnberg, Robert
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The equality case in the substatic Heintze-Karcher inequality
, 2023 We provide a rigidity statement for the equality case for the Heintze-Karcher inequality in substatic manifolds. We apply such result in the warped product setting to fully remove assumption (H4) in the celebrated Brendle's characterization of constant ...
Borghini, Stefano +2 more
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Time-fractional Allen-Cahn equations versus powers of the mean curvature
We show by a formal asymptotic expansion that level sets of solutions of a time-fractional Allen-Cahn equation evolve by a geometric flow whose normal velocity is a positive power of the mean curvature.
Dipierro, Serena +2 more
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A uniqueness and stability principle for surface diffusion
, 2023 We derive a uniqueness and stability principle for surface diffusion before the onset of singularities. The perturbations, however, are allowed to undergo topological changes.
Kroemer, Milan, Laux, Tim
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Rotators-Translators to Mean Curvature Flow in $\mathbb H^2\times\mathbb R$
We establish the existence of one-parameter families of helicoidal surfaces of $\mathbb H^2\times\mathbb R$ which, under mean curvature flow, simultaneously rotate about a vertical axis and translate vertically.Comment: 10 pages, 4 figures.
de Lima, Ronaldo F. +2 more
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Deforming Locally Convex Curves into Curves of Constant $k$-order Width
A nonlocal curvature flow is introduced to evolve locally convex curves in the plane. It is proved that this flow with any initial locally convex curve has a global solution, keeping the local convexity and the elastic energy of the evolving curve, and ...
Gao, Laiyuan +2 more
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Genes expressed in the Drosophila head reveal a role for fat cells in sex-specific physiology. [PDF]
EMBO J, 2002 Fujii S, Amrein H.
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A gain-of-function screen identifying genes required for growth and pattern formation of the Drosophila melanogaster wing. [PDF]
Genetics, 2009 Cruz C, Glavic A, Casado M, de Celis JF.
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