Landau定理中上界的一个改进

通过相关文献给出的穿孔平面C\{0,1}的双曲度量的密度函数的新的下界估计,借助广义Schwarz引理我们对Landau定理中关于上界做了进一步改进并得到了一个带参数的上界表达式.并且当参数取到0时,此结论正好为相关文献得到的结果.     

A bound on local minima of arrangements that implies the upper bound theorem

This paper shows that thei-level of an arrangement of hyperplanes inE ^d has at most local minima. This bound follows from ideas previously used to prove bounds on (≤k)-sets. Using linear programming duality, the Upper Bound Theorem is obtained as a corollary, giving yet another proof of this celebrated bound on the number of vertices of a simple polytope inE ^d withn facets.     

An upper bound for the Folkman number F(3, 3; 5)

Let F(p, q; r) denote the minimum number of vertices in a graph G that has the properties (1) G contains no complete subgraph on r vertices, and (2) any green-red coloring of the edges of G yields a green complete subgraph on p vertices or a red complete subgraph on q vertices. Folkman proved the existence of F(p, q; r) whenever r > max {p, q}. We show F(3, 3; 5) ≤ 17, improving a bound due to Irving and an earlier bound due to Graham and Spencer. © 1993 John Wiley & Sons, Inc.     

An α-approximation theorem for Q∞-manifolds

Given a Q^∞-manifold M and an open cover α of M, there is an open cover β of M such that every β-equivalence from a Q^∞-manifold N to M is α-close to a homeomorphism. Consequently, every Q^∞-deficient subset in a C^∞-manifold M is strongly negligible in M.     

The loop product for 3-manifolds

Let M be a connected, closed, oriented and smooth manifold of dimension d. Let LM be the space of loops in M. Chas and Sullivan introduced the loop product, an associative product of degree ?d on the homology of LM. In this Note we aim at identifying 3-manifolds with “non-trivial” loop products. To cite this article: H. Abbaspour, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Open 3-manifolds whose fundamental groups have infinite center, and a torus theorem for 3-orbifolds

Our main result is a characterization of open Seifert fibered -manifolds in terms of the fundamental group and large-scale geometric properties of a triangulation. As an application, we extend the Seifert Fiber Space Theorem and the Torus Theorem to a class of -orbifolds.

     

Complexity of 3-manifolds and combed 3-manifolds

A new complexity, called a block number, is defined for a combed 3-manifold, and a method for the combinatorial classification of combed 3-manifolds with a given block number is proposed.     

An upper bound for domination number of 5-regular graphs

Let G = (V, E) be a simple graph. A subset S ⊆ V is a dominating set of G, if for any vertex u ∈ V-S, there exists a vertex v ∈ S such that uv ∈ E. The domination number, denoted by γ(G), is the minimum cardinality of a dominating set. In this paper we will prove that if G is a 5-regular graph, then γ(G) ⩽ 5/14n.     

Lower bound theorem for normal pseudomanifolds

In this paper we present a self-contained combinatorial proof of the lower bound theorem for normal pseudomanifolds, including a treatment of the cases of equality in this theorem. We also discuss McMullen and Walkup's generalized lower bound conjecture for triangulated spheres in the context of the lower bound theorem. Finally, we pose a new lower bound conjecture for non-simply connected triangulated manifolds.     

The lower and upper bound problems for cubical polytopes

We construct a family of cubical polytypes which shows that the upper bound on the number of facets of a cubical polytope (given a fixed number of vertices) is higher than previously suspected. We also formulate a lower bound conjecture for cubical polytopes.This paper was researched and written while the author was a graduate student at MIT. The author was partially supported by an NSF Graduate Fellowship.     

A lower bound theorem for polytope pairs

V. Klee has generalized the lower bound theorem of D. Barnette for polytope pairs. He has extensively studied polytope pairs. Here, two theorems for polytope pairs, which are analogous to those of Barnette and lead to more open problems for polytope pairs, are proved. Two theorems of Klee and two of Barnette are immediate corollaries of the theorems.     

Thin position for knots and 3-manifolds

We prove that for 2-bridge knots and 3-bridge knots in thin position the double branched cover inherits a manifold decomposition in thin position. We also argue that one should not expect this sort of correspondence to hold in general.