共查询到18条相似文献,搜索用时 77 毫秒
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本文提出了n维球面型空间和双曲空间中双基本图形的概念,建立了球面型空间与双曲空间中双基图形的度量方程,并给出度量方程的一些应用. 相似文献
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预给二面角的单形在球面型空间Sn,r的嵌入 总被引:3,自引:1,他引:2
本文获得预给二面角的单形嵌入球面型空间Sn,r的一个充分必要条件,并利用它得到关于球面单形二面角的两类几何不等式。 相似文献
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通过几何分析方法与抛物型方程组解的逼近理论,研究特殊空间(一维球面S~1到二维球面S~2)上映射的梯度几何流柯西问题解的存在唯一性.利用能量法和空间本身特有的性质来解决能量守恒的问题,并利用适当的抛物型方程组逼近该梯度几何流,在适当的Sobolev空间中建立先验估计,找到其时间的一致正下界和抛物型方程组一列解的Sobo1ev范数的一致边界,借助于抛物型偏微分方程的理论,以此决定该柯西问题解的存在唯一性. 相似文献
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本文提出并解决了初等图形在球面型空间实现的问题: 预给两两之间度量的几何元素e1,e2…,el-1,el+1,…,eN(ei为点或超平面),初等图形{e1,…,el-1,el+1,…,eN}在球面型空间实现的充分必要条件是什么? 相似文献
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《数学物理学报(A辑)》2020,(3)
设(χ,d,μ)是一个满足上双倍条件和几何双倍条件的非齐度量测度空间.利用非齐度量测度空间的一些特征和不等式技巧,证明了Marcinkiewicz积分算子及其交换子在非齐度量测度空间上的Herz空间以及Herz型Hardy空间上的有界性. 相似文献
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In this paper we investigate some notions of completion of partial metric spaces, including the bicompletion, the Smyth completion, and a new “spherical completion”. Given an auxiliary relation, we show that it arises from a totally bounded partial metric space, and the spherical completion of such a space is its round ideal completion. We also give an example of a totally bounded partial metric space whose bicompletion and Smyth completion are not continuous posets. Finally, we present an example of a totally bounded partial metric giving rise to the Scott and lower topologies of a continuous poset, but whose spherical completion is not a continuous poset. 相似文献
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To each groupN of Heisenberg type one can associate a generalized Siegel domain, which for specialN is a symmetric space. This domain can be viewed as a solvable extensionS =NA ofN endowed with a natural left-invariant Riemannian metric. We prove that the functions onS that depend only on the distance from the identity form a commutative convolution algebra. This makesS an example of a harmonic manifold, not necessarily symmetric. In order to study this convolution algebra, we introduce the
notion of “averaging projector” and of the corresponding spherical functions in a more general context. We finally determine
the spherical functions for the groupsS and their Martin boundary.
Communicated by Guido Weiss 相似文献
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Spherical spline quaternion interpolation has been done on sphere in Euclidean space using quaternions. In this paper, we have done the spline split quaternion interpolation on hyperbolic sphere in Minkowski space using split quaternions and metric Lorentz. This interpolation curve is called spherical spline split quaternion interpolation in Minkowski space (MSquad). 相似文献
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Two Results on Metric Addition in Spherical Space 总被引:1,自引:0,他引:1
We establish the concept of metric addition in spherical space and obtain two related results. 相似文献
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For any 3-manifold M3 and any nonnegative integer g, we give here examples of metrics on M each of which has a sequence of embedded minimal surfaces of genus g and without Morse index bounds. On any spherical space form we construct such a metric with positive scalar curvature. More generally, we construct such a metric with Scal>0 (and such surfaces) on any 3-manifold which carries a metric with Scal>0. 相似文献
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Projectively equivalent metrics, exact transverse line fields and the geodesic flow on the ellipsoid
S. Tabachnikov 《Commentarii Mathematici Helvetici》1999,74(2):306-321
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We extend Velling's approach and prove that the second variation of the spherical areas of a family of domains defines a Hermitian
metric on the universal Teichmüller curve, whose pull-back to Diff +(S
1)/S
1 coincides with the Kirillov metric. We call this Hermitian metric the Velling-Kirillov metric. We show that the vertical
integration of the square of the symplectic form of the Velling-Kirillov metric on the universal Teichmüller curve is the
symplectic form that defines the Weil-Petersson metric on the universal Teichmüller space. Restricted to a finite dimensional
Teichmüller space, the vertical integration of the corresponding form on the Teichmüller curve is also the symplectic form
that defines the Weil-Petersson metric on the Teichmüller space. 相似文献
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In this work we construct subdivision schemes refining general subsets of ? n and study their applications to the approximation of set-valued functions. Differently from previous works on set-valued approximation, our methods are developed and analyzed in the metric space of Lebesgue measurable sets endowed with the symmetric difference metric. The construction of the set-valued subdivision schemes is based on a new weighted average of two sets, which is defined for positive weights (corresponding to interpolation) and also when one weight is negative (corresponding to extrapolation). Using the new average with positive weights, we adapt to sets spline subdivision schemes computed by the Lane–Riesenfeld algorithm, which requires only averages of pairs of numbers. The averages of numbers are then replaced by the new averages of pairs of sets. Among other features of the resulting set-valued subdivision schemes, we prove their monotonicity preservation property. Using the new weighted average of sets with both positive and negative weights, we adapt to sets the 4-point interpolatory subdivision scheme. Finally, we discuss the extension of the results obtained in metric spaces of sets, to general metric spaces endowed with an averaging operation satisfying certain properties. 相似文献