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本文给出了第二类典型城的 Busemann函数.证明了下面的定理:对 R-II(p)中通过0点的任一测地线其中U为 p阶酉方阵,.则由r决定的 Busemann函数为:.其中 为下列矩阵的对角元素: 相似文献
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On a Problem Proposed by Kartsatos 总被引:1,自引:0,他引:1
Zhou Haiyun 《东北数学》1999,(1)
§1.IntroductionandPreliminariesLetXbearealreflexiveBanachspacewithnormandnormalizeddualitymappingJ.Asusual,wesupposethatthesp... 相似文献
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1.引言 设 R2是足够光滑的有界区域,考虑非定常的热传导-对流方程的初边值问题: 问题I.求u=(u1,u2),p,T满足:其中u是流体的速度向量,p为压力,T是温度,v>0是运动粘性系数,λ>0是Groshoff数,j=(0,1)是二维向量,x=(x1,x2). 非定常的热传导一对流方程是大气动力学中的一个重要的方程,这个方程组也称为强迫耗散的非线性系统方程组,其较Navier-Stokes方程多了一个未知函数温度场,它与速度和压力之间存在着复杂的非线性关系.从热动力学可知,任何运动都会产生… 相似文献
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本文研究了R^N中的非线性退化椭圆型方程F(Du,D^2u)+us=f的非负粘性解的存在性,其中s〉0,F满足某些关于p的条件,本文在下面的条件下证明了存在性;1.s〉p-1,f在无穷远处不需要增长条件;2.0〈s≤p-1,f在无穷远处具有某种增长条件。 相似文献
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本文利用尺度‖·‖_(H(p,∞))研究了一般紧Lie群上H ̄p函数的临界阶Bochner-Riesz平均算子的有界性,得到了如下结果:是(H ̄p,H(p,∞))型的,并且其中C为与f及R无关的常数。 相似文献
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该文讨论二维无界带形区域中Navier-Stokes方程其中Ω=(0,d)×R,d>0为一常数,u与p为未知量,其中u=(u1,u2)为速度场,p表示压力.我们证明了当u0∈H,f∈V且f[log(e+|x|2)]1/2∈L2(Ω)时,问题(I)在H中存在整体吸引子A,它是的一个子集.对A的Hausdorff维数与Fractal维数我们也给出了估计. 相似文献
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LetF(u),G(u)beC1-functionalsonaHilbertspaceHandsupu∈HF(u)=∞.LetKbeacompactmetricspaceandletKbeanon-emptyclosedsubset≠K,p∈C(K;H).DenoteFR={u∈H|F(u)R}; ΦR={p∈C(K;FR)|p=ponK};c(R)=infp∈ΦRmaxξ∈KG(p(ξ));c0=maxξ∈KG(p(ξ));Φ∞={p∈C(K;H)|p=ponK};… 相似文献
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本文得出一类形如:-Div(g(|Du|)|Du|^p-2Du+f(x,u))=B(x,u,Du)在一定的条件下在W^1.p空间中的弱解的Holder连续性。 相似文献
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The interplay between two-dimensional percolation growth models and one-dimensional particle processes has been a fruitful source of interesting mathematical phenomena. In this paper we develop a connection between the construction of Busemann functions in the Hammersley last-passage percolation model with i.i.d. random weights, and the existence, ergodicity and uniqueness of equilibrium (or time-invariant) measures for the related (multi-class) interacting fluid system. As we shall see, in the classical Hammersley model, where each point has weight one, this approach brings a new and rather geometrical solution of the longest increasing subsequence problem, as well as a central limit theorem for the Busemann function. 相似文献
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Busemann函数在对完备Riemann流形上的拓扑与几何问题的研究中起作十分重要的作用。而显式求出一个域上的Busemann函数将有助于一些问题的解决。在本文中,我们显式求出了对称空间SU~*(2n)/sp(n)上的Busemann函数。 相似文献
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<正> 設F(x)是隨機變数X的分佈函數,x_1,x_2,…,x_n是對X的n次相互獨立觀測的結果.將n個數據按照數值從小到大排列起來,以x_k代表其中的第k個,我們把原來的結果寫成 相似文献
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V.N. Berestovskii 《Siberian Mathematical Journal》2010,51(6):962-970
We give a solution to the problem posed by Busemann which is as follows: Determine the noncompact Busemann G-spaces such that for every two geodesics there exists a motion taking one to the other. We prove that each of these spaces
is isometric to the Euclidean space or to one of the noncompact symmetric spaces of rank 1 (of negative sectional curvature). 相似文献
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<正> 本文是前文的续作,这里引用的記号与以前是一致的,例如(?)为实或复阵(?)的特征根,A~* 是 A 的共轭转置阵,(?)此外,还引用一些新的记号,(?) 相似文献
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V.N. Berestovskiǐ 《Differential Geometry and its Applications》2011,29(3):299-318
We present short proofs of all known topological properties of general Busemann G-spaces (at present no other property is known for dimensions more than four). We prove that all small metric spheres in locally G-homogeneous Busemann G-spaces are homeomorphic and strongly topologically homogeneous. This is a key result in the context of the classical Busemann conjecture concerning the characterization of topological manifolds, which asserts that every n-dimensional Busemann G-space is a topological n-manifold. We also prove that every Busemann G-space which is uniformly locally G-homogeneous on an orbal subset must be finite-dimensional. 相似文献
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We study the geometry of complete Riemannian manifolds endowed with a weighted measure, where the weight function is of quadratic growth. Assuming the associated Bakry–Émery curvature is bounded from below, we derive a new Laplacian comparison theorem and establish various sharp volume upper and lower bounds. We also obtain some splitting type results by analyzing the Busemann functions. In particular, we show that a complete manifold with nonnegative Bakry–Émery curvature must split off a line if it is not connected at infinity and its weighted volume entropy is of maximal value among linear growth weight functions. 相似文献