共查询到20条相似文献,搜索用时 15 毫秒
1.
J. Cheeger 《Geometric And Functional Analysis》2003,13(1):20-72
((no abstract)) .
Submitted: February 2002, Final version: October 2002. 相似文献
2.
In this paper we obtain a lower bound for the logarithmic Sobolev constant of the operator on C∞(M) given by LU f = Δ f - (?U|?f), where U ? C∞(M), M being a finite dimensional compact Riemannian manifold without boundary, in terms of the spectral gap of LU and the lowest eigenvalue of the operator -LU + V, where V is a function related to U and the Ricci curvature of M. Under suitable conditions and being U ≡ 0, this result improves a previous one by J.-D. DEUSCHEL and D.W. STROOCK (J. Funct. Anal. 92 (1990), 30–48). 相似文献
3.
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
4.
Cédric Villani 《Japanese Journal of Mathematics》2016,11(2):219-263
Synthetic theory of Ricci curvature bounds is reviewed, from the conditions which led to its birth, up to some of its latest developments. 相似文献
5.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(6):645-649
We announce results giving constraints on the singularities of spaces which are Gromov-Hausdorf'f limits of sequences of Riemannian manifolds whose Ricci curvature and volume are bounded from below and whose curvature tensor is bounded in an integral sense. 相似文献
6.
Joseph E. Borzellino 《Proceedings of the American Mathematical Society》1997,125(10):3011-3018
We show that the first betti number of a compact Riemannian orbifold with Ricci curvature and diameter is bounded above by a constant , depending only on dimension, curvature and diameter. In the case when the orbifold has nonnegative Ricci curvature, we show that the is bounded above by the dimension , and that if, in addition, , then is a flat torus .
7.
We prove that Riemannian metrics with an absolute Ricci curvature bound and a conjugate radius bound can be smoothed to having
a sectional curvature bound. Using this we derive a number of results about structures of manifolds with Ricci curvature bounds.
The authors were supported in part by NSF Grant. The first author was also supported in part by Alfred P. Sloan Fellowship
This article was processed by the author using the LATEX style filecljourl from Springer-Verlag. 相似文献
8.
Following Li and Yau (Acta Math 156:153?C201 1986) and similar to Perelman (The entropy formula for the Ricci flow and its geometric applications), we define an energy functional ${\mathcal{J}}$ associated to a smooth function ${\phi}$ on a complete Riemannian manifold. As an application, we deduce integral Ricci curvature upper bounds along modified geodesics for complete steady and shrinking gradient Ricci solitons. 相似文献
9.
10.
In this paper, we study Ricci flow on compact manifolds with a continuous initial metric. It was known from Simon(2002) that the Ricci flow exists for a short time. We prove that the scalar curvature lower bound is preserved along the Ricci flow if the initial metric has a scalar curvature lower bound in the distributional sense provided that the initial metric is W1,pfor some n < p ∞. As an application, we use this result to study the relation between the Yamabe invariant and Ricci flat metr... 相似文献
11.
Chi Li 《Advances in Mathematics》2011,(6):4921
In this short note, based on the work of Wang and Zhu (2004) [8], we determine the greatest lower bounds on Ricci curvature for all toric Fano manifolds. 相似文献
12.
David J. Wraith 《Annals of Global Analysis and Geometry》2014,45(4):319-335
We show that in cohomogeneity 3 there are $G$ -manifolds with any given number of isolated singular orbits and an invariant metric of positive Ricci curvature. We show that the corresponding result is also true in cohomogeneity 5, provided the number of singular orbits is even. 相似文献
13.
We extend several geometrical results for manifolds with lower Ricci curvature bounds to situations where one has integral lower bounds. In particular we generalize Colding's volume convergence results and extend the Cheeger-Colding splitting theorem.
14.
Measure contraction property is one of the possible generalizations of Ricci curvature bound to more general metric measure spaces. In this paper, we discover necessary and sufficient conditions for a three dimensional contact subriemannian manifold to satisfy this property. 相似文献
15.
John Oprea 《Proceedings of the American Mathematical Society》2002,130(3):833-839
This brief note presents refinements of the bounds on the first Betti number and the polynomial growth degree of the fundamental group for manifolds with nonnegative Ricci curvature and infinite fundamental group. These refinements are then sharpened when applied to symplectic manifolds.
16.
17.
Let
and
. We are interested in the lower bounds of the integral:
where h > 0 and
. Using the lower bounds for these integrals we obtain in particular for the so-called Fejér operator
of
the following asymptotic expression
which essentially improves the results concerning the approximation behavior of this operator.
Received: 10 January 2006 相似文献
18.
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
19.
Jean-Pierre Bourguignon 《Japanese Journal of Mathematics》2009,4(1):27-45
In the last thirty years three a priori very different fields of mathematics, optimal transport theory, Riemannian geometry and probability theory, have come together
in a remarkable way, leading to a very substantial improvement of our understanding of what may look like a very specific
question, namely the analysis of spaces whose Ricci curvature admits a lower bound. The purpose of these lectures is, starting
from the classical context, to present the basics of the three fields that lead to an interesting generalisation of the concepts,
and to highlight some of the most striking new developments.
This article is based on the 5th Takagi Lectures that the author delivered at the University of Tokyo on October 4 and 5,
2008. 相似文献
20.
In this paper we define an orientation of a measured Gromov–Hausdorff limit space of Riemannian manifolds with uniform Ricci bounds from below. This is the first observation of orientability for metric measure spaces. Our orientability has two fundamental properties. One of them is the stability with respect to noncollapsed sequences. As a corollary we see that if the cross section of a tangent cone of a noncollapsed limit space of orientable Riemannian manifolds is smooth, then it is also orientable in the ordinary sense, which can be regarded as a new obstruction for a given manifold to be the cross section of a tangent cone. The other one is that there are only two choices for orientations on a limit space. We also discuss relationships between \(L^2\)-convergence of orientations and convergence of currents in metric spaces. In particular for a noncollapsed sequence, we prove a compatibility between the intrinsic flat convergence by Sormani–Wenger, the pointed flat convergence by Lang–Wenger, and the Gromov–Hausdorff convergence, which is a generalization of a recent work by Matveev–Portegies to the noncompact case. Moreover combining this compatibility with the second property of our orientation gives an explicit formula for the limit integral current by using an orientation on a limit space. Finally dualities between de Rham cohomologies on an oriented limit space are proven. 相似文献