Results 41 to 50 of about 5,561,344 (365)
Local entropy and generic multiplicity one singularities of mean curvature flow of surfaces [PDF]
Journal of differential geometry, 2018 In this paper we prove that the generic singularity of mean curvature flow of closed embedded surfaces in $\mathbb R^3$ modelled by closed self-shrinkers with multiplicity has multiplicity one.
Ao Sun
semanticscholar +1 more source
Geometric Mean Curvature Lines on Surfaces Immersed in R3 [PDF]
, 2002 Here are studied pairs of transversal foliations with singularities, defined on the Elliptic region (where the Gaussian curvature $\mathcal K$ is positive) of an oriented surface immersed in $\mathbb R^3$.
Garcia, Ronaldo, Sotomayor, Jorge
core +3 more sources
The global geometry of surfaces with prescribed mean curvature in ℝ³ [PDF]
Transactions of the American Mathematical Society, 2018 We develop a global theory for complete hypersurfaces in R n + 1 \mathbb {R}^{n+1} whose mean curvature is given as a prescribed function of its Gauss map.
Antonio Bueno, J. A. Gálvez, Pablo Mira
semanticscholar +1 more source
Mean Curvature Skeletons [PDF]
Computer Graphics Forum, 2012 AbstractInspired by recent developments in contraction‐based curve skeleton extraction, we formulate the skeletonization problem via mean curvature flow (MCF). While the classical application of MCF is surface fairing, we take advantage of its area‐minimizing characteristic to drive the curvature flow towards the extreme so as to collapse the input ...
Andrea Tagliasacchi +3 more
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Factorable Surfaces in Pseudo-Galilean Space with Prescribed Mean and Gaussian Curvatures
Journal of New Theory, 2022 We study the so-called factorable surfaces in the pseudo-Galilean space, the graphs of the product of two functions of one variable. We then classify these surfaces when the mean and Gaussian curvatures are functions of one variable.
Muhittin Evren Aydın +2 more
doaj +1 more source
Communications in Contemporary Mathematics, 2019 The skew mean curvature flow (SMCF), which origins from the study of fluid dynamics, describes the evolution of a codimension two submanifold along its binormal direction. We study the basic properties of the SMCF and prove the existence of a short-time solution to the initial value problem of the SMCF of compact surfaces in Euclidean space [Formula ...
Song, Chong, Sun, Jun
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Bernstein-type theorems in hypersurfaces with constant mean curvature
Anais da Academia Brasileira de Ciências, 2000 By using the nodal domains of some natural function arising in the study of hypersurfaces with constant mean curvature we obtain some Bernstein-type theorems.
MANFREDO P. DO CARMO, DETANG ZHOU
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Symmetry of hypersurfaces and the Hopf Lemma
Mathematics in Engineering, 2023 A classical theorem of A. D. Alexandrov says that a connected compact smooth hypersurface in Euclidean space with constant mean curvature must be a sphere.
YanYan Li
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Nonfattening of Mean Curvature Flow at Singularities of Mean Convex Type [PDF]
Communications on Pure and Applied Mathematics, 2017 We show that a mean curvature flow starting from a compact, smoothly embedded hypersurface M ⊆ ℝn + 1 remains unique past singularities, provided the singularities are of mean convex type, i.e., if around each singular point, the surface moves in one ...
Or Hershkovits, B. White
semanticscholar +1 more source
Mean Curvature Flow of Mean Convex Hypersurfaces [PDF]
Communications on Pure and Applied Mathematics, 2016 In the last 15 years, White and Huisken‐Sinestrari developed a far‐reaching structure theory for the mean curvature flow of mean convex hypersurfaces. Their papers provide a package of estimates and structural results that yield a precise description of singularities and of high‐curvature regions in a mean convex flow.In the present paper, we give a ...
Haslhofer, Robert, Kleiner, Bruce
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