We investigate the finiteness structure of a complete open Riemannian n-manifold M whose radial curvature at a base point of M is bounded from below by that of a non-compact von Mangoldt surface of revolution with its total curvature greater than π. We show, as our main theorem, that all Busemann functions on M are exhaustions, and that there exists a compact subset of M such that the compact s...

If u ∈ H(M,N) is a weakly J-holomorphic map from a compact without boundary almost hermitian manifold (M, j, g) into another compact without boundary almost hermitian manifold (N, J, h). Then it is smooth near any point x where Du has vanishing Morrey norm M2,2m−2, with 2m =dim(M). Hence H2m−2measure of the singular set for a stationary J-holomorphic map is zero. Blow-up analysis and the energy...

There are many instances of the principle that if A is an algebra of functions on X, then every ring homomorphism A → C is given by evaluation at a particular x ∈ X. Examples are the nullstellensatz in algebraic geometry and the result of Gelfand when X is a compact Hausdorff space. In these cases one can regard X as being included in Hom(A, C) as the set of those f : A → C which satisfy the se...

We introduce new techniques to derive compact descriptions of Golay sequences and their extensions. In particular we show how a fundamental notion of commu-tative algebra, namely the notion of Grr obner bases, can be successfully employed to give compact description of Golay sequences. We then concentrate on the practically important case of Golay sequences of length 2 n. For those sequences we...

In this note we relate two notions of compactness for strongly continuous semigroups of linear operators and cosine functions of linear operators. Specifically, if T denotes a strongly continuous semigroup of linear operators defined on a Banach space X, we will show that T is compact if and only if the set {(T(-)x : x £ X, \\x\\ < 1} is relatively compact in any space LP([Q, a]) ; X) for 1 < p...

The problem of minimal distortion bending of smooth compact embedded connected Riemannian n-manifolds M and N without boundary is made precise by defining a deformation energy functional Φ on the set of diffeomorphisms Diff(M,N). We derive the Euler-Lagrange equation for Φ and determine smooth minimizers of Φ in case M and N are simple closed curves. MSC 2000 Classification: 58E99

We say that a subset of C n is hypoconvex if its complement is the union of complex hyperplanes. Let be the closed unit disk in C , ? = @. We prove two conjectures of Helton and Marshall. Let be a smooth function on ? C n whose sublevel sets have compact hypoconvex bers over ?. Then, with some restrictions on , if Y is the set where is less than or equal to 1, the polynomial convex hull of Y is...

For a compact connected Lie group G acting as isometries of cohomogeneity not equal to 0 or 2 on orientable Riemannian manifold $$M^{n+1},$$ we prove the existence nontrivial embedded G-invariant minimal hypersurface, that is smooth outside set Hausdorff dimension at most $$n-7.$$

Definition. Let X be a metric space with metric d. (a) A collection {G α } α∈A of open sets is called an open cover of X if every x ∈ X belongs to at least one of the G α , α ∈ A. An open cover is finite if the index set A is finite. (b) X is compact if every open cover of X contains a finite subcover. Definition. Let X be a metric space with metric d and let A ⊂ X. We say that A is a compact s...