共查询到20条相似文献,搜索用时 15 毫秒
1.
V.K. Beloshapka 《Journal of Mathematical Analysis and Applications》2011,374(2):655-672
Locally homogeneous CR-manifolds in dimension 3 were classified, up to local CR-equivalence, by E. Cartan. We classify, up to local CR-equivalence, all locally homogeneous CR-manifolds in dimension 4. The classification theorem enables us also to classify all symmetric CR-manifolds in dimension 4, up to local CR-equivalence. 相似文献
2.
The volume preserving mean curvature flow near spheres 总被引:3,自引:0,他引:3
Joachim Escher Gieri Simonett 《Proceedings of the American Mathematical Society》1998,126(9):2789-2796
By means of a center manifold analysis we investigate the averaged mean curvature flow near spheres. In particular, we show that there exist global solutions to this flow starting from non-convex initial hypersurfaces.
3.
Christine M. Escher Shari K. Ultman 《Topology and its Applications》2011,158(1):38-51
In light of recent advances in the study of manifolds admitting Riemannian metrics of positive sectional curvature, the study of certain infinite families of seven dimensional manifolds has become a matter of interest. We determine the cohomology ring structures of manifolds belonging to these families. This particular ring structure indicates the existence of topological invariants distinguishing the corresponding homeomorphism and diffeomorphism type. We show that all families contain representatives of infinitely many homotopy types. 相似文献
4.
Changyu Xia 《Annals of Global Analysis and Geometry》2009,36(1):105-110
Let M be an n-dimensional complete connected Riemannian manifold with sectional curvature sec(M) ≥ 1 and radius rad(M) > π/2. In this article, we show that M is isometric to a round n-sphere if for any x ∈ M, the first conjugate locus of x is a single point and if M contains a geodesic loop of length 2 · rad(M). We also show that the same conclusion is true if the conjugate value function at any point of M is a constant function.
This work was done while the author was visiting MPI for Mathematics in Leipzig, Germany. The author is very grateful to MPI
for Mathematics in Leipzig for its hospitality and CAPES. 相似文献
5.
We give existence results for solutions of the prescribed scalar curvature equation on S3, when the curvature function is a positive Morse function and satisfies an index-count condition. 相似文献
6.
Changyu Xia 《Proceedings of the American Mathematical Society》1997,125(6):1801-1806
Let be an ()-dimensional compact Riemannian manifold with nonnegative Ricci curvature and nonempty boundary . Assume that the principal curvatures of are bounded from below by a positive constant . In this paper, we prove that the first nonzero eigenvalue of the Laplacian of acting on functions on satisfies with equality holding if and only if is isometric to an -dimensional Euclidean ball of radius . Some related rigidity theorems for are also proved.
7.
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.
8.
By variational methods, for a kind of Yamabe problem whose scalar curvature vanishes in the unit ball BN and on the boundary S^N-1 the mean curvature is prescribed, we construct multi-peak solutions whose maxima are located on the boundary as the parameter tends to 0^+ under certain assumptions. We also obtain the asymptotic behaviors of the solutions. 相似文献
9.
A. A. Borisenko 《Mathematical Notes》1997,62(5):562-565
The topological structure of compact Riemannian manifolds that admit hyperbolic foliations is studied.
Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 673–676, November, 1997.
Translated by S. S. Anisov 相似文献
10.
Pui-Fai Leung 《Annals of Global Analysis and Geometry》1995,13(1):55-58
We prove a sufficient condition for a compact hypersurface in Euclidean space to be spherical in terms of a pinching for the Ricci curvature. 相似文献
11.
Enrico Valdinoci 《Journal of Differential Equations》2006,225(2):710-736
We consider an elliptic PDE problem related with fluid mechanics. We show that level sets of rescaled solutions satisfy the zero mean curvature equation in a suitable weak viscosity sense. In particular, such level sets cannot be touched from below (above) by a convex (concave) paraboloid in a suitably small neighborhood. 相似文献
12.
Francesco Mercuri Maria Helena Noronha 《Transactions of the American Mathematical Society》1996,348(7):2711-2724
In this paper we study compact submanifolds of Euclidean space with nonnegative isotropic curvature and low codimension. We determine their homology completely in the case of hypersurfaces and for some low codimensional conformally flat immersions.
13.
14.
We consider the pseudo-Euclidean space , , with coordinates and metric , , where at least one is positive, and also tensors of the form , such that are differentiable functions of x. For such tensors, we use Lie point symmetries to find metrics that solve the Ricci curvature and the Einstein equations. We provide a large class of group-invariant solutions and examples of complete metrics defined globally in . As consequences, for certain functions , we show complete metrics , conformal to the pseudo-Euclidean metric g, whose scalar curvature is . 相似文献
15.
HUANG Xiaojun 《中国科学A辑(英文版)》2006,49(11):1441-1450
In this paper, we discuss some recent studies on the complex structure of an isolated normal singularity by using the information
from its link. We also give some open problems to be further pursued.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
16.
Ch. Xia 《Commentarii Mathematici Helvetici》1999,74(3):456-466
In this paper, we study complete open n-dimensional Riemannian manifolds with nonnegative Ricci curvature and large volume growth. We prove among other things that
such a manifold is diffeomorphic to a Euclidean n-space if its sectional curvature is bounded from below and the volume growth of geodesic balls around some point is not too far
from that of the balls in .
Received: August 17, 1998. 相似文献
17.
Hong Xin Guo 《数学学报(英文版)》2010,26(7):1299-1308
In this paper, we derive evolution equation of the integral of the Gauss curvature on an evolving hypersurface. As an application, we obtain a monotone quantity on the level surface of the potential function on a 3-dimensional steady gradient Ricci soliton with positive sectional curvature, and prove that such a soliton is rotationally symmetric outside of a compact set under a curvature decaying assumption. Along the way we will also apply our evolution equation to some other cases. 相似文献
18.
HUANG Xiaojun Department of Mathematics Rutgers University New Brunswick NJ USA 《中国科学A辑(英文版)》2006,(11)
In this paper, we discuss some recent studies on the complex structure of an isolated normal singularity by using the information from its link. We also give some open problems to be further pursued. 相似文献
19.
Under special conditions that hold for a number of applications, we suggest a construction that reduces the calculation of
algebro-geometric solutions of the zero curvature equation for 2 × 2 matrices to solving the Jacobi inversion problem on a
hyperelliptic Riemann surface and the Riccati equation. An application to the system of equations of the principal chiral
field is considered.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 1, pp. 61–72, January, 1997. 相似文献
20.
We prove an endpoint weak-type maximal inequality for the spherical maximal operator applied to radial funcions on symmetric spaces of constant curvature and dimension . More explicitly, in the Lorentz space associated with the natural isometry-invariant measure, we show that, for every radial function ,
The proof uses only geometric arguments and volume estimates, and applies uniformly in every dimension.
The proof uses only geometric arguments and volume estimates, and applies uniformly in every dimension.