共查询到20条相似文献,搜索用时 15 毫秒
1.
We prove a lower bound estimate for the first non-zero eigenvalue of the Witten–Laplacian on compact Riemannian manifolds. As an application, we derive a lower bound estimate for the diameter of compact gradient shrinking Ricci solitons. Our results improve some previous estimates which were obtained by the first author and Sano (Asian J Math, to appear), and by Andrews and Ni (Comm Partial Differential Equ, to appear). Moreover, we extend the diameter estimate to compact self-similar shrinkers of mean curvature flow. 相似文献
2.
William Wylie 《Proceedings of the American Mathematical Society》2008,136(5):1803-1806
We show that if a complete Riemannian manifold supports a vector field such that the Ricci tensor plus the Lie derivative of the metric with respect to the vector field has a positive lower bound, then the fundamental group is finite. In particular, it follows that complete shrinking Ricci solitons and complete smooth metric measure spaces with a positive lower bound on the Bakry-Emery tensor have finite fundamental group. The method of proof is to generalize arguments of García-Río and Fernández-López in the compact case.
3.
New lower bounds of the first nonzero eigenvalue of the weighted p-Laplacian are established on compact smooth metric measure spaces with or without boundaries. Under the assumption of positive lower bound for the m-Bakry–Émery Ricci curvature, the Escobar–Lichnerowicz–Reilly type estimates are proved; under the assumption of nonnegative ∞-Bakry–Émery Ricci curvature and the m-Bakry–Émery Ricci curvature bounded from below by a non-positive constant, the Li–Yau type lower bound estimates are given. The weighted p-Bochner formula and the weighted p-Reilly formula are derived as the key tools for the establishment of the above results. 相似文献
4.
We give a sharp upper diameter bound for a compact shrinking Ricci soliton in terms of its scalar curvature integral and the Perelman’s entropy functional. The sharp cases could occur at round spheres. The proof mainly relies on a sharp logarithmic Sobolev inequality of gradient shrinking Ricci solitons and a Vitali-type covering argument.
相似文献5.
对紧致Riemannian流形(无边或带有凸边界)的第一(Neumann)特征值,用流形的直径和Ricci曲率的下界,给出一些新的下界估计. 相似文献
6.
In this paper,we study steady Ricci solitons with a linear decay of sectional curvature.In particular,we give a complete classification of 3-dimensional steady Ricci solitons and 4-dimensional K-noncollapsed steady Ricci solitons with non-negative sectional curvature under the linear curvature decay. 相似文献
7.
We show that recent work of Ni and Wilking (in preparation) [11] yields the result that a noncompact nonflat Ricci shrinker has at most quadratic scalar curvature decay. The examples of noncompact Kähler–Ricci shrinkers by Feldman, Ilmanen, and Knopf (2003) [7] exhibit that this result is sharp. We also prove a similar result for certain noncompact steady gradient Ricci solitons. 相似文献
8.
Shi Jin Zhang 《数学学报(英文版)》2011,27(5):871-882
In this note, we obtain a sharp volume estimate for complete gradient Ricci solitons with scalar curvature bounded below by
a positive constant. Using Chen-Yokota’s argument we obtain a local lower bound estimate of the scalar curvature for the Ricci
flow on complete manifolds. Consequently, one has a sharp estimate of the scalar curvature for expanding Ricci solitons; we
also provide a direct (elliptic) proof of this sharp estimate. Moreover, if the scalar curvature attains its minimum value
at some point, then the manifold is Einstein. 相似文献
9.
Zhongmin Qian 《Bulletin des Sciences Mathématiques》2009,133(2):145-168
In this paper we consider Hamilton's Ricci flow on a 3-manifold with a metric of positive scalar curvature. We establish several a priori estimates for the Ricci flow which we believe are important in understanding possible singularities of the Ricci flow. For Ricci flow with initial metric of positive scalar curvature, we obtain a sharp estimate on the norm of the Ricci curvature in terms of the scalar curvature (which is not trivial even if the initial metric has non-negative Ricci curvature, a fact which is essential in Hamilton's estimates [R.S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982) 255-306]), some L2-estimates for the gradients of the Ricci curvature, and finally the Harnack type estimates for the Ricci curvature. These results are established through careful (and rather complicated and lengthy) computations, integration by parts and the maximum principles for parabolic equations. 相似文献
10.
11.
Thomas Ivey 《Proceedings of the American Mathematical Society》1997,125(4):1203-1208
We classify the Kähler metrics on compact manifolds of complex dimension two that are solitons for the constant-volume Ricci flow, assuming that the curvature is slightly more positive than that of the single known example of a soliton in this dimension.
12.
We prove precompactness in an orbifold Cheeger–Gromov sense of complete gradient Ricci shrinkers with a lower bound on their
entropy and a local integral Riemann bound. We do not need any pointwise curvature assumptions, volume or diameter bounds.
In dimension four, under a technical assumption, we can replace the local integral Riemann bound by an upper bound for the
Euler characteristic. The proof relies on a Gauss–Bonnet with cutoff argument. 相似文献
13.
In this paper, we study gradient solitons to the Ricci flow coupled with harmonic map heat flow. We derive new identities on solitons similar to those on gradient solitons of the Ricci flow. When the soliton is compact, we get a classification result. We also discuss the relation with quasi-Einstein manifolds. 相似文献
14.
We study the injectivity radius bound for 3-d Ricci flow with bounded curvature. As applications, we show the long time existence of the Ricci flow with positive Ricci curvature and with curvature decay condition at infinity. We partially settle a question of Chow-Lu-Ni [Hamilton’s Ricci Flow, p. 302]. 相似文献
15.
Satyaki Dutta 《Advances in Mathematics》2010,224(2):525-538
In this paper, we prove that under a lower bound on the Ricci curvature and an assumption on the asymptotic behavior of the scalar curvature, a complete conformally compact manifold whose conformal boundary is the round sphere has to be the hyperbolic space. It generalizes similar previous results where stronger conditions on the Ricci curvature or restrictions on dimension are imposed. 相似文献
16.
In this paper, we study the evolution of L
2 one forms under Ricci flow with bounded curvature on a non-compact Rimennian manifold. We show on such a manifold that the L
2 norm of a smooth one form is non-increasing along the Ricci flow with bounded curvature. The L
∞ norm is showed to have monotonicity property too. Then we use L
∞ cohomology of one forms with compact support to study the singularity model for the Ricci flow on
. 相似文献
17.
Jun Ling 《Annals of Global Analysis and Geometry》2007,31(4):385-408
We give new estimates on the lower bounds for the first closed and Neumann eigenvalues for compact manifolds with positive
Ricci curvature in terms of the diameter and the lower bound of Ricci curvature. The results sharpen the previous estimates.
相似文献
18.
Recently, in [49], a new definition for lower Ricci curvature bounds on Alexan-drov spaces was introduced by the authors. In this article, we extend our research to summarize the geometric and analytic results under this Ricci condition. In particular, two new results, the rigidity result of Bishop-Gromov volume comparison and Lipschitz continuity of heat kernel, are obtained. 相似文献
19.
Recently, in [49], a new definition for lower Ricci curvature bounds on Alexandrov spaces was introduced by the authors. In this article, we extend our research to summarize the geometric and analytic results under this Ricci condition. In particular, two new results, the rigidity result of Bishop-Gromov volume comparison and Lipschitz continuity of heat kernel, are obtained. 相似文献
20.
A. Engoulatov 《Journal of Functional Analysis》2006,238(2):518-529
We derive a gradient estimate for the logarithm of the heat kernel on a Riemannian manifold with Ricci curvature bounded from below. The bound is universal in the sense that it depends only on the lower bound of Ricci curvature, dimension and diameter of the manifold. Imposing a more restrictive non-collapsing condition allows one to sharpen this estimate for the values of time parameter close to zero. 相似文献