The isovariant Borsuk Ulam constant cc of a compact Lie group G is defined to be the supremum of c ∈ R such that the inequalityc（dim V - dim V^C） ≤ dim W - dim W^Gholds whenever there exists a G-isovariant map f ...The isovariant Borsuk Ulam constant cc of a compact Lie group G is defined to be the supremum of c ∈ R such that the inequalityc（dim V - dim V^C） ≤ dim W - dim W^Gholds whenever there exists a G-isovariant map f ： S（V） → S（W） between G-representation spheres. In this paper, we shall discuss some properties of cG and provide lower estimates of cG of connected compact Lie groups, which leads us to some Borsuk-Ulam type results for isovariant maps. We also introduce and discuss the generalized isovariant Borsuk-Ulam constant c^-G for more general smooth G-actions on spheres. The result is considerably different from the case of linear actions.展开更多
In this report, we shall discuss the calculations of degree of equivariant mappings about Z_p actions and give a generalization of Borsuk-Ulam theorem about Z_p actions. At first, some notations are introduced. For no...In this report, we shall discuss the calculations of degree of equivariant mappings about Z_p actions and give a generalization of Borsuk-Ulam theorem about Z_p actions. At first, some notations are introduced. For nonnegative integers m,n,〈m,n〉 denotes the greatest common divisor of m and n. m|n means that m is a factor of n. We fix a positive integer p, and展开更多
In 1957,Hadwiger made a conjecture that every n-dimensional convex body can be covered by 2n translates of its interior.Up to now,this conjecture is still open for all n 3.In 1933,Borsuk made a conjecture that every n...In 1957,Hadwiger made a conjecture that every n-dimensional convex body can be covered by 2n translates of its interior.Up to now,this conjecture is still open for all n 3.In 1933,Borsuk made a conjecture that every n-dimensional bounded set can be divided into n + 1 subsets of smaller diameters.Up to now,this conjecture is open for 4 n 297.In this article we encode the two conjectures into continuous functions defined on the spaces of convex bodies,propose a four-step program to attack them,and obtain some partial results.展开更多
An isovariant map is an equivariant map preserving the isotropy subgroups. In this paper, we develop an isovariant version of the Hopf classification theorem; namely, an isovariant homotopy classification result of G-...An isovariant map is an equivariant map preserving the isotropy subgroups. In this paper, we develop an isovariant version of the Hopf classification theorem; namely, an isovariant homotopy classification result of G-isovariant maps from free G-manifolds to representation spheres under a certain dimensional condition, the so-called Borsuk-Ulam inequality. In order to prove it, we use equivariant obstruction theory and the multidegree of an isovariant map.展开更多
By the generalized Borsuk theorem in coincidence degree theory, a p-Laplacian neutral functional differential equation is studied. A new result on the existence of periodic solution is obtained. The interest is that s...By the generalized Borsuk theorem in coincidence degree theory, a p-Laplacian neutral functional differential equation is studied. A new result on the existence of periodic solution is obtained. The interest is that some coeffcient in it is not a constant function and its sign can be changeable, which is different from that in the known literatures.展开更多
文摘The isovariant Borsuk Ulam constant cc of a compact Lie group G is defined to be the supremum of c ∈ R such that the inequalityc（dim V - dim V^C） ≤ dim W - dim W^Gholds whenever there exists a G-isovariant map f ： S（V） → S（W） between G-representation spheres. In this paper, we shall discuss some properties of cG and provide lower estimates of cG of connected compact Lie groups, which leads us to some Borsuk-Ulam type results for isovariant maps. We also introduce and discuss the generalized isovariant Borsuk-Ulam constant c^-G for more general smooth G-actions on spheres. The result is considerably different from the case of linear actions.
文摘In this report, we shall discuss the calculations of degree of equivariant mappings about Z_p actions and give a generalization of Borsuk-Ulam theorem about Z_p actions. At first, some notations are introduced. For nonnegative integers m,n,〈m,n〉 denotes the greatest common divisor of m and n. m|n means that m is a factor of n. We fix a positive integer p, and
基金Supported by Natural Science Foundation of Education Department of Anhui Province (KJ2010B353)Young Teacher’s Foundation of Anhui Normal University (2008xqn46)
基金supported by National Natural Science Foundation of China (Grant No.10225104)the Chang Jiang Scholars Program and LMAM at Peking University
文摘In 1957,Hadwiger made a conjecture that every n-dimensional convex body can be covered by 2n translates of its interior.Up to now,this conjecture is still open for all n 3.In 1933,Borsuk made a conjecture that every n-dimensional bounded set can be divided into n + 1 subsets of smaller diameters.Up to now,this conjecture is open for 4 n 297.In this article we encode the two conjectures into continuous functions defined on the spaces of convex bodies,propose a four-step program to attack them,and obtain some partial results.
文摘An isovariant map is an equivariant map preserving the isotropy subgroups. In this paper, we develop an isovariant version of the Hopf classification theorem; namely, an isovariant homotopy classification result of G-isovariant maps from free G-manifolds to representation spheres under a certain dimensional condition, the so-called Borsuk-Ulam inequality. In order to prove it, we use equivariant obstruction theory and the multidegree of an isovariant map.
基金supported by Natural Science Foundation of Education Department of Anhui Province (No.KJ2010B353)Young Teacher’s Foundation of Anhui Normal University (No.2008xqn46)
文摘By the generalized Borsuk theorem in coincidence degree theory, a p-Laplacian neutral functional differential equation is studied. A new result on the existence of periodic solution is obtained. The interest is that some coeffcient in it is not a constant function and its sign can be changeable, which is different from that in the known literatures.
