Spherical Minimal Immersions with Prescribed Codimension

We describe a general construction of manufacturing new spherical minimal immersions between round spheres out of old ones. The new immersions have higher domain dimension and degree and the construction has a precise control on the codimension. Applied to classified and recent examples, the construction gives an abundance of new spherical minimal immersions with prescribed codimensions.Mathematics Subject Classifications (2000). 53C42     

Minimal rambling sets with codimension one dominated splittings

In this paper,we study the dynamics of minimal rambling sets with codimension one dominatedsplittings     

Uniqueness of Minimal Projections in Smooth Matrix Spaces

Let X=(M(n, m), ·), where · fulfills Condition 0.3 and W=M(n, 1)+M(1, m). A formula for a minimal projection from X onto W is given in (E. W. Cheney and W. A. Light, 1985, “Approximation Theory in Tensor Product Spaces,” Lecture Notes in Mathematics, Springer-Verlag, Berlin; E. J. Halton and W. A. Light, 1985, Math. Proc. Cambridge Philos. Soc.97, 127–136; and W. A. Light, 1986, Math. Z.191, 633–643). We will show that this projection is the unique minimal projection (see Theorem 2.1).     

New Construction for Spherical Minimal Immersions

We describe a general method of manufacturing new minimal immersions between round spheres out of old ones. The resulting spherical minimal immersions are given analytically in terms of the harmonic projection operator and have higher source dimensions. Applied to classical examples, this gives an abundance of new minimal immersions of even-dimensional spheres.     

一致极小对,一致有界性及有穷基定理

本文使用最小板块的思想，揭示了泛代数领域中任一分配簇的任一代数都具有两个性质；（１）投射意义下一致极小对是存在的。（２）存在相对于整个族而言的极小对投射的一致上界。用以上的结果，给出了著名的有穷基定理的一个简单的、构造性的证明。     

Hyperinterpolation on the Sphere at the Minimal Projection Order

We investigate hyperinterpolation operators based on positive weighted quadrature rules, as introduced by Ian H. Sloan. If the rules are exact of double degree then, independently of the number of their nodes, the operator norms increase at the order of the minimal projections.     

Notes on Smooth Map Germs

ＮｏｔｅｓｏｎＳｍｏｏｔｈＭａｐＧｅｒｍｓＹｕＬｉ（余立）；ＺｈａｎｇＧｕｏｂｉｎ（张国滨）（ＺｈａｎｊｉａｎｇＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｓｔｕｄｙｔｈｅｄｅｔｅｒｍｉｎａｃｙｏｆｒｅａ...     

Constants of Strong Uniqueness of Minimal Projections onto Hyperplanes in the Space ℓ∞ n (n≥3)

In this paper, we obtain the maximum values of the constants of strong uniqueness of minimal projections with nonunit norm on hyperplanes in the space #x2113; ⁿ (n3)     

Surfaces in $${\mathbb {P}^{4}}$$ fibered in cubics

Any algebraic surface in which is fibered in cubics, so that the generic fibre is a twisted cubic, gives rise to a curve Γ in a suitable compactification X of the space of smooth rational cubics of In this paper the case n = 4 is addressed and the corresponding space X is studied. We apply our results to complete the classification of smooth, rational surfaces in ruled in cubics. This work is within the framework of the national research project “Geometry on Algebraic Varieties” Cofin 2006 of MIUR.     

Corrigenda to “Barth type vanishing theorems”

We fix a mistake contained in a previous paper concerning vanishing theorems for low codimensional varieties in . This work is within the framework of the national research project “Geomety on Algebraic Varieties” Cofin 2008 of MIUR.     

De Morgan代数同余格的性质

以弱射影为工具，得到了ＤｅＭｏｒｇａｎ代数的主同余关系的刻划，在此基础上证明了同余格θ（Ｌ）为原子的充要条件是Ｌ为弱原子的。然后通过引进极小商的概念，描述了θ（Ｌ）是布尔格的Ｄｅ Ｍｏｒｇａｎ代数Ｌ。     

Vector spaces as unions of proper subspaces

In this note, we find a sharp bound for the minimal number (or in general, indexing set) of subspaces of a fixed (finite) codimension needed to cover any vector space V over any field. If V is a finite set, this is related to the problem of partitioning V into subspaces.     

Some computations of algebraic cycle homology

We compute the algebraic cycle homology for codimension 1 cycles on a variety over a perfect field; our computation agrees with Nart's computation of Bloch's higher Chow groups for codimension 1 cycles. We interpret algebraic cycle homology in terms of sheaves for Voevodsky's h-topology and use this to adapt a recent result of Suslin-Voevodsky: we establish for a complex variety that algebraic cycle homology with Z/n coefficients is naturally isomorphic to singular homology with Z/n coefficients.Partially supported by the NSF and NSA Grant #MDA904-90-H-4006.     

Splitting Obstruction Groups in Codimension 2

The splitting obstruction groups depend functorially on the square of fundamental groups. In the paper the problem of splitting along a submanifold of codimension two under some restrictions on the square of fundamental groups is considered. New exact sequences and commutative diagrams containing Wall groups, splitting obstruction groups, and surgery obstruction groups for manifold pairs are obtained. Examples of computation of splitting obstruction groups and natural maps are considered.