到欧氏空间的等距极小浸入

本文研究了欧氏空间极小子流形的测地球的体积增长,给出了一个黎曼流形可等距极小浸入到欧氏空间的一个必要条件,并给出了具非正截曲率的欧氏空间极小超曲面的一个分类．     

Finding minimal spanning trees in a euclidean coordinate space

The minimal spanning tree problem of a point set in ak-dimensional Euclidean space is considered and a new version of the multifragmentMST-algorithm of Bentley and Friedman is given. The minimal spanning tree is found by repeatedly joining the minimal subtree with the closest subtree. Ak-d tree is used for choosing the connecting edges. Computation time of the algorithm depends on the configuration of the point set: for normally distributed random points the algorithm is very fast. Two extreme cases demandingO(n logn) andO(n ²) operations,n being the cardinality of the point set, are also given.     

On minimal graph evolutions in the hyperbolic space

We study here minmal graph evolutions in the hyperbolic space and prove that there exists a unique smooth solution. This work is partially supported by NNSF of China     

On the worst case of a minimal spanning tree algorithm for euclidean space

This paper concerns the worst case running time of the minimal spanning tree algorithm presented by Bentley and Friedman. For a set ofN points ink-dimensional Euclidean space the worst case performance of the algorithm is shown to beΘ(N ² logN), fork≧2 andΘ(N ²), fork=1.     

Minimal isometric immersions of inhomogeneous spherical space forms into spheres--- a necessary condition for existence

Although much is known about minimal isometric immersions into spheres of homogeneous spherical space forms, there are no results in the literature about such immersions in the dominant case of inhomogeneous space forms. For a large class of these, we give a necessary condition for the existence of such an immersion of a given degree. This condition depends only upon the degree and the fundamental group of the space form and is given in terms of an explicitly computable function. Evaluating this function shows that neither nor admit a minimal isometric immersion into any sphere if the degree of the immersion is less than , or less than , respectively.

     

On a property of minimal triangulations

A graph H has the property MT, if for all graphs G, G is H-free if and only if every minimal (chordal) triangulation of G is H-free. We show that a graph H satisfies property MT if and only if H is edgeless, H is connected and is an induced subgraph of P₅, or H has two connected components and is an induced subgraph of 2P₃.This completes the results of Parra and Scheffler, who have shown that MT holds for H=P_k, the path on k vertices, if and only if k?5 [A. Parra, P. Scheffler, Characterizations and algorithmic applications of chordal graph embeddings, Discrete Applied Mathematics 79 (1997) 171-188], and of Meister, who proved that MT holds for ?P₂, ? copies of a P₂, if and only if ??2 [D. Meister, A complete characterisation of minimal triangulations of 2K₂-free graphs, Discrete Mathematics 306 (2006) 3327-3333].     

How a minimal surface leaves a thin obstacle

We prove the optimal regularity and a detailed analysis of the free boundary of the solutions to the thin obstacle problem for nonparametric minimal surfaces with flat obstacles.     

On a minimal complex norm that extends the real euclidean norm

A minimal extension of the real euclidean norm to ⁿ is introduced and some complex analytic properties of its unit ball are studied.Research supported partially by Fulbright Grant (1986–1987) at Universität Osnabrück-Abteilung Vechta.     

关于Lapleca算子的大特征值

在两种情下，给出了Laplace算子大特征值的的上界估计，改进了两个已有的结果。     

On the number of minimal models of a log smooth threefold

We give a topological bound on the number of minimal models of a class of three-dimensional log smooth pairs of log general type.     

On the convergence behavior of conformal immersion sequence from cylinders

In this paper, we are concerned with the convergence behavior of a sequence of conformal immersions {fn} from long cylinders Pn with Pn|Afn|2+ μ(fn(Pn)) Λ. We show that if {fn} does not converge to a point, the total Gauss curvatures and the measures of the images of {fn} will not lose on the necks and each neck consists of a point.     

On the maximum size of minimal definitive quartet sets

In this paper, we investigate a problem concerning quartets; a quartet is a particular kind of tree on four leaves. Loosely speaking, a set of quartets is said to be ‘definitive’ if it completely encapsulates the structure of some larger tree, and ‘minimal’ if it contains no redundant information. Here, we address the question of how large a minimal definitive quartet set on n leaves can be, showing that the maximum size is at least 2n−8 for all n≥4. This is an enjoyable problem to work on, and we present a pretty construction, which employs symmetry.     

On a free boundary problem and minimal surfaces

From minimal surfaces such as Simons' cone and catenoids, using refined Lyapunov–Schmidt reduction method, we construct new solutions for a free boundary problem whose free boundary has two components. In dimension 8, using variational arguments, we also obtain solutions which are global minimizers of the corresponding energy functional. This shows that the theorem of Valdinoci et al. [41], [42] is optimal.