排序方式: 共有23条查询结果,搜索用时 15 毫秒
1.
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
2.
We first prove stochastic representation formulae for space–time harmonic mappings defined on manifolds with evolving Riemannian metric. We then apply these formulae to derive Liouville type theorems under appropriate curvature conditions. Space–time harmonic mappings which are defined globally in time correspond to ancient solutions to the harmonic map heat flow. As corollaries, we establish triviality of such ancient solutions in a variety of different situations. 相似文献
3.
We use versions of Bismut type derivative formulas obtained by Driver and Thalmaier [9], to prove derivative estimates for various heat semigroups on Riemannian vector bundles. As an application, the weak (1,1) property for a class of Riesz transforms on a vector bundle is established. Some concrete examples of vector bundles (e.g., differential forms) are considered to illustrate the results. 相似文献
4.
In this article, functional inequalities for diffusion semigroups on Riemannian manifolds (possibly with boundary) are established, which are equivalent to pinched Ricci curvature, along with gradient estimates, \(L^p\)-inequalities and log-Sobolev inequalities. These results are further extended to differential manifolds carrying geometric flows. As application, it is shown that they can be used in particular to characterize general geometric flow and Ricci flow by functional inequalities. 相似文献
5.
The Liouville property of a complete Riemannian manifold M (i.e., the question whether there exist non-trivial bounded harmonic functions on M) attracted a lot of attention. For Cartan–Hadamard manifolds the role of lower curvature bounds is still an open problem.
We discuss examples of Cartan–Hadamard manifolds of unbounded curvature where the limiting angle of Brownian motion degenerates
to a single point on the sphere at infinity, but where nevertheless the space of bounded harmonic functions is as rich as
in the non-degenerate case. To see the full boundary the point at infinity has to be blown up in a non-trivial way. Such examples
indicate that the situation concerning the famous conjecture of Greene and Wu about existence of non-trivial bounded harmonic
functions on Cartan–Hadamard manifolds is much more complicated than one might have expected.
相似文献
6.
We prove Cheng–Yau type inequalities for positive harmonic functions on Riemannian manifolds by using methods of Stochastic Analysis. Rather than evaluating an exact Bismut formula for the differential of a harmonic function, our method relies on a Bismut type inequality which is derived by an elementary integration by parts argument from an underlying submartingale. It is the monotonicity inherited in this submartingale which allows us to establish the pointwise estimates. 相似文献
7.
We consider the Itô stochastic differential equation on Rd. The diffusion coefficients A1,…,Am are supposed to be in the Sobolev space with p>d, and to have linear growth. For the drift coefficient A0, we distinguish two cases: (i) A0 is a continuous vector field whose distributional divergence δ(A0) with respect to the Gaussian measure γd exists, (ii) A0 has Sobolev regularity for some p′>1. Assume for some λ0>0. In case (i), if the pathwise uniqueness of solutions holds, then the push-forward #(Xt)γd admits a density with respect to γd. In particular, if the coefficients are bounded Lipschitz continuous, then Xt leaves the Lebesgue measure Lebd quasi-invariant. In case (ii), we develop a method used by G. Crippa and C. De Lellis for ODE and implemented by X. Zhang for SDE, to establish existence and uniqueness of stochastic flow of maps. 相似文献
8.
Ferenc Móricz Ulrich Stadtmüller Monika Thalmaier 《Journal of Theoretical Probability》2008,21(3):660-671
We consider random fields and introduce a concept of ℳ-dependence for random fields. Using a lemma from summability theory
we prove strong laws of large numbers for blockwise ℳ-dependent random fields under various moment conditions, thereby generalizing
some results in the literature from independent random fields.
This research was started while the first author visited the University of Ulm, Institute of Number Theory & Probability Theory
in October 2006; and it was also supported by the Hungarian National Foundation for Scientific Research under Grant T 046192. 相似文献
9.
In this article, new curvature conditions are introduced to establish functional inequalities including gradient estimates, Harnack inequalities and transportation-cost inequalities on manifolds with non-convex boundary. 相似文献
10.