Showing papers in "Advances in Mathematics in 1991"

TL;DR: In this article, the correctness of appropriate string diagrams for various kinds of monoidal categories with duals has been proved for various classes of classes of subject classes, including algebra, geometry, physics, and astronomy.

TL;DR: In this article, a boundary problem for Riemannian Einstein metrics is studied, where the conformal class [S] is defined as the conformality of a metric on a compact (n + l)-dimensional manifold with bounding boxes.

TL;DR: In this paper, the authors deal with non-commutative objects based on the Weyl algebra from the differential geometric point of view, where the basic object is not a point of a space but certain sections of bundles.

TL;DR: In this paper, it was shown that all H-type groups which possess certain geometric properties, clearly possessed by Iwasawa N-groups, satisfy a Lie-algebraic condition (implicit in the work of B. Kostant [Kt2]) that we shall call the J'-condition.

TL;DR: In this article, it was shown that Kostka-Foulkes polynomials (or certain Kazhdan-Lusztig polynomial for the affine Weyl group of type A) are matrix coefficients on the space V.

TL;DR: The notion of affine surface area was introduced by Clauset as discussed by the authors and has been used extensively in the area of polytope approximation, where it has been shown that polytopes have zero afftne surface area.

TL;DR: In this article, it was shown that in general non-linear quasi-states will exist on C (X ), where X is a compact Hausdorff space, and the concept of a quasi-measure in X and established the connection between quasi-state and quasi-measures.

TL;DR: In this paper, a notion for hypersurfaces in R d + 1 that is analogous to the chord-arc condition with small constant for curves in the plane is introduced, and various equivalent operator-theoretic, function-and geometrical characterizations of these surfaces are given.

TL;DR: The key result in this article is a proof of a large class of identities, generalizing the Capelli identity, which is a centerpiece of 19th century invariant theory, which asserts the equality of two differential operators on the n 2-dimensional space M(n, R) of n x n real matrices.

TL;DR: In this article, it was shown that the number of PGL(2, C) equivalence classes of degree d rational maps with a fixed branch set is generically equal to the Catalan number ϱ(d) = ( 1 d )( 2d−2 d−1 ).

TL;DR: In this paper, the authors present a different approach to the analysis of the spectrum of a compact surface of constant negative curvature, which is quite different from that in the Selberg approach, and suggest that there is some mechanism involving a Perron-Frobenius type operator characterizing the Laplacian spectrum of the surface.

TL;DR: In this article, Dress and Wenzel showed that a matroid with coefficients of finite rank can also be defined in terms of its associated Grassmann-Plucker map, which generalizes classical determinants.

TL;DR: In this article, the authors show that these surfaces must be homeomorphic to R d, and they build parameterizations with L p bounds on the gradient, and the gradient of the inverse, with p → ∞ as the chord-arc constant goes to 0.

TL;DR: In this article, the Hahn-Banach theorem is reformulated in a way which may be applied equally to questions of continuity and equivariance, to yield the information which is traditionally intended when applying the Axiom of Choice.

TL;DR: In this article, the Gauss-Green theorem for any bounded set of bounded variation and any bounded vector field continuous outside a set of σ-finite (m − 1)-dimensional Hausdorff measures was established.

TL;DR: In this article, the authors characterized and classified the Hk-conjugacy classes of maximalk-split tori for non-algebraically closed fields, where the base field is the real numbers, p -adic numbers, finite fields, and number fields.

TL;DR: In this article, the authors define a (sequential) recession functional, which is a topological vector space topological mapping where the mapping F,(u) = inf lim inf i f(tnun) -:t,+ + + al,u,P,u ) n-+m t, I where (t, and u) are sequences.

TL;DR: In this paper, the authors introduce four conjectures refining a very useful result of Mark Green's on the linear part of the free resolution of a graded module over a polynomial ring.

TL;DR: The Lie integral as mentioned in this paper is a non-linear integral defined for Lie algebra valued functions in terms of the representations of the algebra, and its properties are investigated in the context of differential equations.

TL;DR: In this paper, the authors give an introductory, rather detailed description of these interesting groups, and discuss some further structure on these groups, the computations of Floer homology for the Brieskorn homology 3-spheres by Fintushel and Stern, and the relation with Donaldson polynomials for 4-manifolds.

TL;DR: In this article, it was shown that the set of matrices T jl = c(j)−c(l) j−l a(j), l a(l), b(j, l) 0 0 1 with j, l arbitrary integers is closed under multiplication.

TL;DR: In this article, the authors consider real-valued functions defined on the interval [0, 1] and denote by Δ the set of derivatives; i.e., if there is a differentiable function F such that F' = ƒ, any such function is a primitive of ǫ and is uniquely determined up to a constant.