We study the properties of certain affine invariant measures of symmetry associated to a compact convex body L in a Euclidean vector space. As functions of the interior of L, these measures of symmetry are proved or disproved to be concave in specific situations, notably for the reduced moduli of spherical minimal immersions. MSC 2000: 53C42

B.Y. Chen Null 2-type surfaces in Euclidean space, Algebra, Analysis and Geometry, Taipei, World Scientiic 1989, 1-18] initiated the study of submanifolds whose mean curvature vector H is an eigenvector of the Laplacian. In this article, we study this problem for minimal surfaces in CP n. Two classiication theorems are obtained.

This paper shows that the general hypersurface of degree ≥ 6 in projective four space cannot support an indecomposable rank two vector bundle which is Arithmetically CohenMacaulay and four generated. Equivalently, the equation of the hypersurface is not the Pfaffian of a four by four minimal skewsymmetric matrix.

A minimal set of generators of the ring of invariants for four linear subspaces of dimension n in a vector space of dimension 2n is computed, using the symbolic method introduced by Grosshans et al. [Grosshans, F., Rota, G.-C. & Stein, J. A. (1987) Invariant Theory and Superalgebras (Am. Math. Soc., Providence, RI)].

In this article we develop a new approach to duality theory for convex vector optimization problems. We modify a given (set-valued) vector optimization problem such that the image space becomes a complete lattice (a sublattice of the power set of the original image space), where the corresponding infimum and supremum are sets that are related to the set of (minimal and maximal) weakly efficient...