共查询到20条相似文献,搜索用时 15 毫秒
1.
We prove some sharp isoperimetric type inequalities in warped product manifolds, or more generally, multiply warped product manifolds. We also relate them to inequalities involving the higher order mean-curvature integrals. Applications include some sharp eigenvalue estimates, Pólya-Szegö inequality, Faber-Krahn inequality, Sobolev inequality and some sharp geometric inequalities in some warped product spaces. 相似文献
2.
Julian Scheuer 《Journal of Functional Analysis》2019,276(4):1097-1144
The long-time existence and umbilicity estimates for compact, graphical solutions to expanding curvature flows are deduced in Riemannian warped products of a real interval with a compact fibre. Notably we do not assume the ambient manifold to be rotationally symmetric, nor the radial curvature to converge, nor a lower bound on the ambient sectional curvature. The inverse speeds are given by powers of a curvature function satisfying few common properties. 相似文献
3.
We introduce a new existence result for compact normal geodesic graphs with constant mean curvature and boundary in a class
of warped product spaces. In particular, our result includes that of normal geodesic graphs with constant mean curvature in
hyperbolic space over a bounded domain in a totally geodesic .
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4.
We consider the closed orientable hypersurfaces in a wide class of warped product manifolds, which include space forms, deSitter-Schwarzschild and Reissner-Nordström manifolds. By using an integral formula or Brendle's Heintze-Karcher type inequality, we present some new characterizations of umbilic hypersurfaces. These results can be viewed as generalizations of the classical Jellet-Liebmann theorem and the Alexandrov theorem in Euclidean space. 相似文献
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Simon Brendle 《Publications Mathématiques de L'IHéS》2013,117(1):247-269
We consider surfaces with constant mean curvature in certain warped product manifolds. We show that any such surface is umbilic, provided that the warping factor satisfies certain structure conditions. This theorem can be viewed as a generalization of the classical Alexandrov theorem in Euclidean space. In particular, our results apply to the deSitter-Schwarzschild and Reissner-Nordstrom manifolds. 相似文献
8.
Heudson Mirandola 《Geometriae Dedicata》2009,138(1):117-127
This work states some half-space type theorems in a warped product space of the form I ×ρ
M, where is an open interval and M is either a compact n-manifold, or a complete simply connected surface with constant curvature c ≤ 0. Such theorems generalize the classical half-space theorem for minimal surfaces in R
3, obtained by Hoffmann and Meeks (Invent Math 101:373–377, 1990), and recent results for surfaces contained in a slab of R ×ρ
M, obtained by Dajczer and Alías (Comment Math Helvetici 81:653–663, 2006).
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Maciej P. Wojtkowski 《Proceedings of the American Mathematical Society》2005,133(11):3395-3402
We provide a list of all locally metric Weyl connections with nonpositive sectional curvatures on two types of manifolds, -dimensional tori and with the standard conformal structures. For we prove that it carries no other Weyl connections with nonpositive sectional curvatures, locally metric or not. In the case of we prove the same in the more narrow class of integrable connections.
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Ruy Tojeiro 《Geometriae Dedicata》2007,128(1):17-31
We prove a decomposition theorem for conformal immersions \(f\colon\;M^n\to {\mathbb{R}}^{N}\) into Euclidean space of a warped product of Riemannian manifolds \(M^n:=M_0\times_\rho\Pi_{i=1}^k M_i\) of dimension n ≥ 3 under the assumption that the second fundamental form \(\alpha \colon TM \times TM\to T^\perp M\) of f satisfies \(\alpha|_{TM_i\times TM_j}=0\) for i ≠ j. It generalizes the corresponding theorem of Nölker for isometric immersions as well as our previous result on conformal immersions of Riemannian products. In particular, we determine all conformal representations of Euclidean space of dimension n ≥ 3 as a warped product of Riemannian manifolds. As a consequence, we classify the conformally flat warped products. 相似文献
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Luis Guijarro Gerard Walschap 《Proceedings of the American Mathematical Society》2008,136(4):1419-1425
We study several properties of the Sharafutdinov dual foliation in open manifolds with nonnegative sectional curvature.
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In this paper, we first investigate several rigidity problems for hypersurfaces in the warped product manifolds with constant linear combinations of higher order mean curvatures as well as “weighted” mean curvatures, which extend the work (Brendle in Publ Math Inst Hautes Études Sci 117:247–269, 2013; Brendle and Eichmair in J Differ Geom 94(94):387–407, 2013; Montiel in Indiana Univ Math J 48:711–748, 1999) considering constant mean curvature functions. Secondly, we obtain the rigidity results for hypersurfaces in the space forms with constant linear combinations of intrinsic Gauss–Bonnet curvatures $L_k$ . To achieve this, we develop some new kind of Newton–Maclaurin type inequalities on $L_k$ which may have independent interest. 相似文献
16.
We investigate existence and uniqueness of solutions of the Cauchy problem for the porous medium equation on a class of Cartan–Hadamard manifolds. We suppose that the radial Ricci curvature, which is everywhere nonpositive as well as sectional curvatures, can diverge negatively at infinity with an at most quadratic rate: in this sense it is referred to as critical. The main novelty with respect to previous results is that, under such hypotheses, we are able to deal with unbounded initial data and solutions. Moreover, by requiring a matching bound from above on sectional curvatures, we can also prove a blow-up theorem in a suitable weighted space, for initial data that grow sufficiently fast at infinity. 相似文献
17.
Hu Zejun 《数学学报(英文版)》1998,14(3):361-370
We study the conformal deformation for prescribing scalar curvature function
on Cartan-Hadamard manifoldM
n
(n≥3) with strongly negative curvature. By employing the supersubsolution method and a careful construction for the supersolution,
we obtain the best possible asymptotic behavior for
near infinity so that the problem of complete conformal deformation is solvable. In more general cases, we prove an asymptotic
estimation on the solutions of the conformal scalar curvature equation.
Project partially supported by the NNSF of China 相似文献
18.
Chi-Keung Cheung 《Mathematische Zeitschrift》1989,201(1):105-119
Research partially supported by National Science Foundation 相似文献
19.
Yi SHI . Guanghan LI . Chuarixi WU 《数学年刊B辑(英文版)》2014,35(1):93-100
In this paper, the relationship between the existence of closed geodesics and the volume growth of complete noncompact Riemannian manifolds is studied. First the authors prove a diffeomorphic result of such an n-m2nifold with nonnegative sectional curvature, which improves Marenich-Toponogov's theorem. As an application, a rigidity theorem is obtained for nonnegatively curved open manifold which contains a clesed geodesic. Next the authors prove a theorem about the nonexistence of closed geodesics for Riemannian manifolds with sectional curvature bounded from below by a negative constant. 相似文献
20.
Wei-jun Lu 《高校应用数学学报(英文版)》2013,28(2):240-252
In this paper, we study f-harmonicity of some special maps from or into a doubly warped product manifold. First we recall some properties of doubly twisted product manifolds. After showing that the inclusion maps from Riemannian manifolds M and N into the doubly warped product manifold M × μ,λ N can not be proper f-harmonic maps, we use projection maps and product maps to construct nontrivial f-harmonic maps. Thus we obtain some similar results given in [21], such as the conditions for f-harmonicity of projection maps and some characterizations for non-trivial f-harmonicity of the special product maps. Furthermore, we investigate non-trivial f-harmonicity of the product of two harmonic maps. 相似文献