R~n中的一个Bonnesen型不等式

研究了n维欧氏空间中凸体K的等周亏格的下界估计,即Bonnesen型不等式.首先加强了Lutwak中得到的关于凸体K的p-平均不等式,用此得到一个用凸体K的均质积分及调和均质积分表示的等周亏格的下界估计.     

欧氏空间E~n中Euler不等式的加强推广(英文)

The relation between the circum-radius and the in-radius of an n-dimensional simplex in E~n is studied.Two new generalizations of Euler inequality for the n-dimensional simplex are established.Besides,we obtain some stronger generalizations of Euler inequality for the n-dimensional simplex than previously known results.     

Minkowski空间的等价性定理及在Finsler几何的应用

首先利用中心仿射几何中的结果建立了Minkowski空间的等价性定理.作为在Finsler几何中的应用,我们证明满足一定条件的Landsberg空间为Berwald空间,这些条件可以是具有闭的Cartan型形式,S曲率为零或平均Berwald曲率为零.     

E~n空间中k-n型Neuberg-Pedoe不等式

本文首先利用基本求导法则,证明了涉及单形的n-1维与n维体积的一个几何不等式,由此便得到En空间中k-n型Neuberg-Pedoe不等式.     

Hlder不等式和Minkowski不等式的推广

本文利用变分方法对多个变元的不含变元导数的Holder不等式和Minkowski不等式进行了推广．此种方法的主要意义不在于证明传统的不等式，而在于发现新的不等式．     

同向单形到欧氏空间的等距嵌入及其应用

该文利用矩阵的方法, 获得了两个同向的 n 维单形同时等距嵌入 Eⁿ 维欧氏空间的一个充分必要条件是: 对于预给(n+1)²个距离,满足一组具有行列式形式的不等式组det(△_k)<0, 由此可以得到两组等数量的有限点集合到 Eⁿ 维欧氏空间中等长嵌入的一个充分必要条件. 然后利用杨路和张景中引进的代数方法, 应用广义等距嵌入定理, 提出了关于两组两个完全同向的 n 维单形“广义度量加”的概念, 并且证明了涉及“广义度量加”的一个几何不等式, 它推广了杨路和张景中关于Alexander猜想的结果. 同时我们将杨路和张景中关于Neuberg-Pedoe不等式的高维推广形式推广到两组两个完全同向的 n 维单形中, 获得了涉及四个单形的一类几何不等式, 它们蕴含近期诸多文献的主要结果.     

Properties of Mappings Related to the Minkowski Inequality

In this paper we obtain properties of several mappings which are arisen from the Minkowski inequality. We investigate superadditivity (subadditivity) and monotonicity of those functions, and give some refinements of the Minkowski inequality and the H?lder inequality.     

A Reilly Type Inequality for the First Eigenvalue of Finsler Submanifolds in Minkowski Space

In this paper, we study the extrinsic upper bound for the first eigenvalue of compact Finsler submanifolds in Minkowski space and obtain a Reilly type inequality. It is reduced to the standard Reilly inequality when the ambient space is Euclidean.Mathematics Subject Classification (1991): 53C60, 53B40.     

Criteria for Balance in Abelian Gain Graphs, with Applications to Piecewise-Linear Geometry

Consider a gain graph with abelian gain group having no odd torsion. If there is a basis of the graph’s binary cycle space, each of whose members can be lifted to a closed walk whose gain is the identity, then the gain graph is balanced, provided that the graph is finite or the group has no non-trivial infinitely 2-divisible elements. We apply this theorem to deduce a result on the projective geometry of piecewise-linear realizations of cell-decompositions of manifolds.     

广义Minkowski不等式的进一步改进

针对"亚正定阵理论(Ⅱ)"一文的广义Minkowski不等式不成立问题,在已有的修正结果基础上,给出一种完整的修正结果;并更正了"亚正定阵的几个开问题及一些不等式"一文中有关的错误结论;用反例说明"广义正定矩阵的进一步研究"一文中的有关结论是错误的,给出完整的修正结果.     

Hlder不等式和Minkowski不等式的推广

本文利用变分方法对多个变元的不含变元导数的H■lder不等式和Minkowski不等式进行了推广．此种方法的主要意义不在于证明传统的不等式,而在于发现新的不等式．     

高维欧氏空间中的广义度量方程及其应用

本文利用代数的方法，证明了：对于两个等数量有限基本元素构成的集合，杨路和张景中关于高维欧氏空间E^n中的度量方程仍然成立，得到了一个广义度量方程，其特殊情况就是著名的Cayley定理．作为初步应用，给出了两个单形外接超球球心距和棱切超球球心距的两个公式.     

从球面到欧几里得空间的连续映射的性质及其应用

In this paper, we study the property of continuous mappings from a sphere to the Euclidean space. By using the theory of the periodic transformation in algebraic topology, we obtain a generalized Borsuk-Ulam theorem and then give some applications of the theorem.     

关于双曲空间中n维Pedoe不等式及应用

本文应用距离几何的理论与方法,研究了双曲空间中n维单形的几何不等式问题,建立了双曲空间中涉及两个单形棱长的n维Pedoe不等式和彭-常不等式,由此获得双曲空间n维单形的一些新的不等式.     

Geometry of Two- and Three-Dimensional Minkowski Spaces

A class of centrally-symmetric convex 12-topes (12-hedrons) in is described such that for an arbitrary prescribed norm on each polyhedron in the class can be inscribed in (circumscribed about) the -ball via an affine transformation, and this can be done with large degree of freedom. Bibliography: 5 titles.     

投影阵在空间解析几何中的应用

本文得到了空间直线和平面的投影阵，并举例说明了它在空间解析几何中的应用。     

Properties and Applications of the Distance Functions on Open Sets of the Euclidean Space

Russian Mathematics - For an open subset of the Euclidean space of dimension n we consider interior and exterior approximations by sequences of open sets. We prove convergence everywhere of the...