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Uniqueness and Pseudolocality Theorems of the Mean Curvature Flow
, 2006 Mean curvature flow evolves isometrically immersed base manifolds $M$ in the direction of their mean curvatures in an ambient manifold $\bar{M}$. If the base manifold $M$ is compact, the short time existence and uniqueness of the mean curvature flow are ...
Chen, Bing-Long, Yin, Le
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Is mean curvature flow a gradient flow?
, 2023 It is well-known that the mean curvature flow is a formal gradient flow of the perimeter functional. However, by the work of Michor and Mumford [7,8], the formal Riemannian structure that is compatible with the gradient flow structure induces a degenerate metric on the space of hypersurfaces.
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Mean curvature flow of spacelike graphs [PDF]
Mathematische Zeitschrift, 2010 version 5: Math.Z (online first 30 July 2010). version 4: 30 pages: we replace the condition $K_1\geq 0$ by the the weaker one $Ricci_1\geq 0$. The proofs are essentially the same. We change the title to a shorter one.
Li, Guanghan, Salavessa, Isabel M. C.
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FEBS Letters, EarlyView.We reconstituted Synechocystis glycogen synthesis in vitro from purified enzymes and showed that two GlgA isoenzymes produce glycogen with different architectures: GlgA1 yields denser, highly branched glycogen, whereas GlgA2 synthesizes longer, less‐branched chains.
Kenric Lee +3 more
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Diffuse-interface approximation and weak–strong uniqueness of anisotropic mean curvature flow
European Journal of Applied MathematicsThe purpose of this paper is to derive anisotropic mean curvature flow as the limit of the anisotropic Allen–Cahn equation. We rely on distributional solution concepts for both the diffuse and sharp interface models and prove convergence using relative ...
Tim Laux +2 more
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Mean curvature flow of monotone Lagrangian submanifolds
, 2006 We use holomorphic disks to describe the formation of singularities in the mean curvature flow of monotone Lagrangian submanifolds in $\mathbb C^{n}$.Comment: 37 pages, 3 ...
G. Huisken +13 more
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Highly degenerate harmonic mean curvature flow [PDF]
Calculus of Variations and Partial Differential Equations, 2008 We study the evolution of a weakly convex surface $ _0$ in $\R^3$ with flat sides by the Harmonic Mean Curvature flow. We establish the short time existence as well as the optimal regularity of the surface and we show that the boundaries of the flat sides evolve by the curve shortening flow.
Caputo, M. C., Daskalopoulos, P.
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Dual targeting of RET and SRC synergizes in RET fusion‐positive cancer cells
Molecular Oncology, EarlyView.Despite the strong activity of selective RET tyrosine kinase inhibitors (TKIs), resistance of RET fusion‐positive (RET+) lung cancer and thyroid cancer frequently occurs and is mainly driven by RET‐independent bypass mechanisms. Son et al. show that SRC TKIs significantly inhibit PAK and AKT survival signaling and enhance the efficacy of RET TKIs in ...
Juhyeon Son +13 more
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A geometric flow on null hypersurfaces of Lorentzian manifolds
Topological Algebra and its Applications, 2022 We introduce a geometric flow on a screen integrable null hypersurface in terms of its local second fundamental form. We use it to give an alternative proof to the vorticity free Raychaudhuri’s equation for null hypersurface, as well as establishing ...
Massamba Fortuné, Ssekajja Samuel
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The extension and convergence of mean curvature flow in higher codimension [PDF]
, 2011 In this paper, we first investigate the integral curvature condition to extend the mean curvature flow of submanifolds in a Riemannian manifold with codimension $d\geq1$, which generalizes the extension theorem for the mean curvature flow of ...
Liu, Kefeng +3 more
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