共查询到18条相似文献,搜索用时 15 毫秒
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杜伟平 《高校应用数学学报(A辑)》2005,20(2):225-232
设M为(n 1)维流形Ⅳ中完备、非紧、定向的、具有常平均曲率H的强稳定超曲面,文中证明了若Ⅳ的双Ricci曲率沿M不小于-n^2H^2,则M上不存在非平凡的L^2调和1-形式. 相似文献
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Luis J. Alí as Aldir Brasil Jr. Oscar Perdomo 《Proceedings of the American Mathematical Society》2007,135(11):3685-3693
Barbosa, do Carmo and Eschenburg characterized the totally umbilical spheres as the only weakly stable compact constant mean curvature hypersurfaces in the Euclidean sphere . In this paper we prove that the weak index of any other compact constant mean curvature hypersurface in n+1 which is not totally umbilical and has constant scalar curvature is greater than or equal to , with equality if and only if is a constant mean curvature Clifford torus with radius .
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Luis J. Alías 《Journal of Mathematical Analysis and Applications》2010,363(2):579-630
In this paper we study the behavior of the scalar curvature S of a complete hypersurface immersed with constant mean curvature into a Riemannian space form of constant curvature, deriving a sharp estimate for the infimum of S. Our results will be an application of a weak Omori-Yau maximum principle due to Pigola, Rigoli, Setti (2005) [17]. 相似文献
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We prove that many complete, noncompact, constant mean curvature (CMC) surfaces
are nondegenerate; that is, the Jacobi operator Δf + | Af |2 has no L2 kernel. In fact, if ∑ has genus zero with k ends, and if f (∑) is embedded (or Alexandrov immersed) in a half-space, then we find an explicit upper bound for the dimension of the L2 kernel in terms of the number of non-cylindrical ends. Our main tool is a conjugation operation on Jacobi fields which linearizes
the conjugate cousin construction. Consequences include partial regularity for CMC moduli space, a larger class of CMC surfaces
to use in gluing constructions, and a surprising characterization of CMC surfaces via spinning spheres.
R.K. partially supported by NSF grants DMS-0076085 at GANG/UMass and DMS-9810361 at MSRI, and by a FUNCAP grant in Fortaleza,
Brazil. J.R. partially supported by an NSF VIGRE grant at Utah.
Received: January 2005; Accepted: June 2005 相似文献
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In this paper, we study locally projectively flat Finsler metrics with constant flag curvature K. We prove those are totally determined by their behaviors at the origin by solving some nonlinear PDEs. The classifications when K=0, K=−1 and K=1 are given respectively in an algebraic way. Further, we construct a new projectively flat Finsler metric with flag curvature K=1 determined by a Minkowski norm with double square roots at the origin. As an application of our main theorems, we give the classification of locally projectively flat spherical symmetric Finsler metrics much easier than before. 相似文献
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Manuel Ritoré Antonio Ros 《Transactions of the American Mathematical Society》1996,348(1):391-410
It is proved that the spaces of index one minimal surfaces and stable constant mean curvature surfaces with genus greater than one in (non fixed) flat three manifolds are compact in a strong sense: given a sequence of any of the above surfaces we can extract a convergent subsequence of both the surfaces and the ambient manifolds in the topology. These limits preserve the topological type of the surfaces and the affine diffeomorphism class of the ambient manifolds. Some applications to the isoperimetric problem are given.
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In this paper, we consider the heat flow for the Hsystem with constant mean curvature in higher dimensions. We give sufficient conditions on the initial data such that the heat flow develops finite time singularity. We also provide a new set of initial data to guarantee the existence of global regular solution to the heat flow, that converges to zero in W 1,n with the decay rate t 2/(2-n) as time goes to infinity. 相似文献
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By using the method of integrable system, we study the deformation of constant mean curvature surfaces in three-dimensional hyperbolic space form H3. We also obtain a Weierstrass representation formula of the constant mean curvature surfaces with mean curvature greater than 1. 相似文献
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Hilá rio Alencar Harold Rosenberg Walcy Santos 《Proceedings of the American Mathematical Society》2004,132(12):3731-3739
In this work we consider connected, complete and orientable hypersurfaces of the sphere with constant nonnegative -mean curvature. We prove that under subsidiary conditions, if the Gauss image of is contained in a closed hemisphere, then is totally umbilic.
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By using the method of integrable system, we study the deformation of constant mean curvature surfaces in three-dimensional
hyperbolic space form H3. We also obtain a Weierstrass representation formula of the constant mean curvature surfaces with mean curvature greater
than 1 相似文献
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This paper is concerned with the motion of a time‐dependent hypersurface ?Ω(t) in ?d that evolves with a normal velocity where κ is the mean curvature of ?Ω(t), and g is an external forcing term. Phase field approximation of this motion leads to the Allen–Cahn equation where ε is an approximation parameter, W a double well potential and cW a constant that depends only on W. We study here a modified version of this equation and we prove its convergence to the same geometric motion. We then make use of this modified equation in the context of mean curvature flow with conservation of the volume, and we show that it has better volume‐preserving properties than the traditional nonlocal Allen–Cahn equation. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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Vidmantas Bentkus 《Journal of Theoretical Probability》1994,7(2):211-224
LetF be the distribution function of a sumS
n ofn independent centered random variables, denote the standard normal distribution function and its density. It follows from our results that
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Sungwook Lee 《Annals of Global Analysis and Geometry》2006,29(4):355-401
It is shown that timelike surfaces of constant mean curvature ± in anti-de Sitter 3-space ?3 1(?1) can be constructed from a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in ?SL2? via Bryant type representation formulae. These Bryant type representation formulae are used to investigate an explicit one-to-one correspondence, the so-called Lawson–Guichard correspondence, between timelike surfaces of constant mean curvature ± 1 and timelike minimal surfaces in Minkowski 3-space E 3 1. The hyperbolic Gauß map of timelike surfaces in ?3 1(?1), which is a close analogue of the classical Gauß map is considered. It is discussed that the hyperbolic Gauß map plays an important role in the study of timelike surfaces of constant mean curvature ± 1 in ?3 1(?1). In particular, the relationship between the Lorentz holomorphicity of the hyperbolic Gauß map and timelike surface of constant mean curvature ± 1 in ?3 1(?1) is studied. 相似文献
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José A. Gálvez Asun Jiménez Pablo Mira 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(6):1631-1644
We give a classification of non-removable isolated singularities for real analytic solutions of the prescribed mean curvature equation in Minkowski 3-space. 相似文献
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In this paper, we investigate complete spacelike hypersurfaces in the de Sitter space with constant k-th mean curvature and two distinct principal curvatures one of which is simple. We obtain some characterizations of the Riemannian product H1(c1)×Sn−1(c2) or Hn−1(c1)×S1(c2) in the de Sitter space . 相似文献
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We prove that if for the curved n-body problem the masses are given, the minimum distance between the point masses of a specific type of relative equilibrium solution to that problem has a universal lower bound that is not equal to zero. We furthermore prove that the set of all such relative equilibria is compact. This class of relative equilibria includes all relative equilibria of the curved n -body problem in H2 and a significant subset of the relative equilibria for S2, S3 and H3. 相似文献
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