共查询到10条相似文献,搜索用时 78 毫秒
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Non-spherical hypersurfaces inE
4 with non-zero constant mean curvature and constant scalar curvature are the only hypersurfaces possessing the following property: Its position vector can be written as a sum of two non-constant maps, which are eigenmaps of the Laplacian operator with corresponding eigenvalues the zero and a non-zero constant. 相似文献
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Let Mn be an n-dimensional complete connected and oriented hypersurface in a hyperbolic space Hn+1(c) with non-zero constant mean curvature H and two distinct principal curvatures. In this paper, we show that (1) if the multiplicities of the two distinct principal curvatures are greater than 1,then Mn is isometric to the Riemannian product Sk(r)×Hn-k(-1/(r2 + ρ2)), where r > 0 and 1 < k < n - 1;(2)if H2 > -c and one of the two distinct principal curvatures is simple, then Mn is isometric to the Riemannian product Sn-1(r) × H1(-1/(r2 +ρ2)) or S1(r) × Hn-1(-1/(r2 +ρ2)),r > 0, if one of the following conditions is satisfied (i) S≤(n-1)t22+c2t-22 on Mn or (ii)S≥ (n-1)t21+c2t-21 on Mn or(iii)(n-1)t22+c2t-22≤ S≤(n-1)t21+c2t-21 on Mn, where t1 and t2 are the positive real roots of (1.5). 相似文献
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Frank Duzaar 《manuscripta mathematica》1996,91(1):303-315
Summary We consider—in the setting of geometric measure theory—hypersurfacesT (of codimension one) with prescribed boundaryB in Euclideann+1 space which maximize volume (i.e.T together with a fixed hypersurfaceT
0 encloses oriented volume) subject to a mass constraint. We prove existence and optimal regularity of solutionsT of such variational problems and we show that, on the regular part of its support,T is a classical hypersurface of constant mean curvature. We also prove that the solutionsT become more and more spherical as the valuem of the mass constraint approaches ∞.
This work was done at the Centre for Mathematics and its Applications at the Australian National University, Canberra while
the author was a visiting member
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag. 相似文献
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Jorge H. S. de Lira Marcelo Melo 《Calculus of Variations and Partial Differential Equations》2014,50(1-2):335-364
We formulate a variational notion of anisotropic mean curvature for immersed hypersurfaces of arbitrary Riemannian manifolds. Hypersurfaces with constant anisotropic mean curvature are characterized as critical points of an elliptic parametric functional subject to a volume constraint. We provide examples of such hypersurfaces in the case of rotationally invariant functionals defined in product spaces. These examples include rotationally invariant hypersurfaces and graphs. 相似文献
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In this article, we prove the following theorem: A complete hypersurface of the hyperbolic space form, which has constant mean curvature and non-negative Ricci curvature Q, has non-negative sectional curvature. Moreover, if it is compact, it is a geodesic distance sphere; if its soul is not reduced to a point, it is a geodesic hypercylinder; if its soul is reduced to a point p, its curvature satisfies Q<, and the geodesic spheres centered at p are convex, then it is a horosphere.A part of this work has been done when the second author visited Université Claude Bernard Lyon 1, and was supported by a grant of the People's Republic of China. 相似文献
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利用流形的紧致性,研究了单位球面Sn+1(1)中具有常平均曲率的紧致超曲面上的Schrodinger算子,讨论了此算子的最小特征值与子流形结构之间的联系,并得到了相应的定理,证明过程比相关文献更简单. 相似文献
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Hypersurfaces with constant scalar curvature 总被引:38,自引:0,他引:38