Results 1 to 10 of about 5,121,571 (362)
Non-existence of eternal solutions to Lagrangian mean curvature flow with non-negative Ricci curvature [PDF]
arXiv, 2016 In this paper, we derive a mean curvature estimate for eternal solutions (including translating solutions) of almost-calibrated Lagrangian mean curvature flow in complex Euclidean space. As a consequence, we show a non-existence result for eternal solutions of almost-calibrated Lagrangian mean curvature flow.
arxiv
Graphs with Parallel Mean Curvature [PDF]
Proceedings of the American Mathematical Society, 1989 We prove that if the graph Γ f = { ( x , f ( x ) ) :
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Gyroids of Constant Mean Curvature [PDF]
Experimental Mathematics, 1997 We use Brakke's Surface Evolver to deform a triply periodic minimal surface, the gyroid, into a continuous family of constant mean curvature surfaces with the same symmetry. We discuss stability and bifurcation problems for these surfaces.
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Polynomial affine translation surfaces in Euclidean 3-space
Boletim da Sociedade Paranaense de Matemática, 2019 In this paper we study the polynomial affine translation surfaces in E3 with constant curvature. We derive some non-existence results for such surfaces. Several examples are also given by figures.
Hülya Gün Bozok, Mahmut Ergüt
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Non-preserved curvature conditions under constrained mean curvature flows [PDF]
arXiv, 2014 We provide explicit examples which show that mean convexity (i.e. positivity of the mean curvature) and positivity of the scalar curvature are non-preserved curvature conditions for hypersurfaces of the Euclidean space evolving under either the volume- or the area preserving mean curvature flow.
arxiv
Ground state solutions for the Hénon prescribed mean curvature equation
Advances in Nonlinear Analysis, 2018 In this paper, we consider the analogous of the Hénon equation for the prescribed mean curvature problem in ℝN{{\mathbb{R}^{N}}}, both in the Euclidean and in the Minkowski spaces. Motivated by the studies of Ni and Serrin [W. M. Ni and J.
Azzollini Antonio
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Non-collapsing in mean-convex mean curvature flow [PDF]
arXiv, 2011 We provide a direct proof of a non-collapsing estimate for compact hypersurfaces with positive mean curvature moving under the mean curvature flow: Precisely, if every point on the initial hypersurface admits an interior sphere with radius inversely proportional to the mean curvature at that point, then this remains true for all positive times in the ...
arxiv
Singular perturbations of mean curvature flow
Journal of Differential Geometry, 2007 We introduce a regularization method for mean curvature flow of a submanifold of arbitrary codimension in the Euclidean space, through higher order equations. We prove that the regularized problems converge to the mean curvature flow for all times before the first singularity.
GIOVANNI BELLETTINI +2 more
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An a priori estimate for the Gauss curvature of nonparametric surfaces of constant mean curvature [PDF]
, 1972 Joel Spruck
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