Results 251 to 260 of about 381,931 (282)

Complete Hypersurfaces with Constant Mean Curvature and Finite Total Curvature

Annals of Global Analysis and Geometry, 1998
Let \(x:M^n \to \overline {M}^{n+1}(c) \) be an isometric immersion of a complete hypersurface into a simply connected complete Riemannian manifold \(\overline {M}^{n+1}(c) \) with constant sectional curvature \(c\) \((c\leq 0)\). We denote by \(A\) and \(H\) the Weingarten endomorphism and the mean curvature of \(M^n .\) The hypersurface \(M^n\) is ...
Bérard, Pierre, do Carmo, Manfredo, Santos, W.   +2 more
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SCALAR CURVATURE OF HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN UNIT SPHERES

International Journal of Mathematics, 2011
Let M be an n-dimensional closed hypersurface with constant mean curvature H in a unit sphere Sn+1, n ≤ 8, and S the squared length of the second fundamental form of M. If |H| ≤ ε(n), then there exists a positive constant α(n, H), which depends only on n and H, such that if S0 ≤ S ≤ S0 + α(n, H), then S ≡ S0 and M is isometric to a Clifford ...
Chen, Gangyi, Li, Haizhong
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Curvature inequalities and rigidity for constant mean curvature and spacetime constant mean curvature surfaces

We establish curvature inequalities and rigidity results for surfaces satisfying constant mean curvature type conditions in both Riemannian and Lorentzian geometry. In the Riemannian setting we study constant mean curvature (CMC) surfaces in three-dimensional manifolds with scalar curvature bounds.
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Surfaces of the Constant Mean Curvature

2015
“Soap bubble” may be called a physical system which is modeled by a surface of constant mean curvature in Euclidian three-dimensional space R 3.
S. N. Krivoshapko, V. N. Ivanov
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Submanifolds with constant mean curvature

Boletim da Sociedade Brasileira de Matemática, 1983
Consider a Riemannian manifold isometrically immersed into a Riemannian manifold of constant sectional curvature such that the mean curvature vector field is parallel, the norm of the second fundamental form is constant, and a certain natural identity is satisfied.
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Computing surface of constant mean curvature with singularities

Computing, 1984
A finite element method is presented for the approximation of minimal surfaces with constant mean curvature. The surfaces are composed of several sheets meeting to form a singular curve. The results are compared against examples that have an exact solution.
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Conformal metrics of the ball with constant 𝜎_{𝑘}-curvature and constant boundary mean curvature

Proceedings of the American Mathematical Society
On the upper hemisphere, we use the Obata-Escobar argument to classify conformal metrics with constant $σ_k$ curvature and constant boundary mean curvature in all types of cones including positive and negative cones. This extends a result of Escobar in \cite{Es} for $k=1$.
Chen, Xuezhang, Wei, Wei
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Constant Mean Curvature Tori

1991
Constant mean curvature tori in ℝ3 were first discovered, in 1984, by Wente [15]. These examples solved the long standing problem of Hopf [6]: Is a compact constant mean curvature surface in ℝ3 necessarily a round sphere? Hopf proved that if the surface is topologically a sphere then it must be round and Alexandrov [3] proved that if the surface is ...
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On the generalized Chern conjecture for hypersurfaces with constant mean curvature in a sphere

Science China Mathematics, 2021
Li Lei
exaly  

Submanifolds with Constant Mean Curvature II

American Journal of Mathematics, 1974
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