Related papers: Compactifications of unstable N\"obeling spaces

We show that an n-dimensional compactum X embeds in R^m, where m>3(n+1)/2, if and only if X x X - \Delta admits an equivariant map to S^{m-1}. In particular, X embeds in R^{2n}, n>3, iff the top power of the (twisted) Euler class of the…

We construct several examples of compactification of Type IIB theory on orientifolds and discuss their duals. In six dimensions we obtain models with $N=1$ supersymmetry, multiple tensor multiplets, and different gauge groups. In nine…

We are interested in contractible n-manifolds M which "split" as M = A union B where A,B, and A intersect B are all homeomorphic to Euclidean n-space (such M are called open n-splitters) or A,B, and A intersect B are all homeomorphic to the…

We study nuclear embeddings for function spaces of generalised smoothness defined on a bounded Lipschitz domain $\Omega\subset\mathbb{R}^d$. This covers, in particular, the well-known situation for spaces of Besov and Triebel-Lizorkin…

For n bodies moving in Euclidean d-space under the influence of a homogeneous pair interaction we compactify every center-of-mass energy surface, obtaining a 2d(n -1)-1 - dimensional manifold with corners in the sense of Melrose. After a…

The local classification of Kaehler submanifolds $M^{2n}$ of the hyperbolic space $\mathbb{H}^{2n+p}$ with low codimension $2\leq p\leq n-1$ under only intrinsic assumptions remains a wide open problem. The situation is quite different for…

We study a modified version of Lerman-Whitehouse Menger-like curvature defined for m+2 points in an n-dimensional Euclidean space. For 1 <= l <= m+2 and an m-dimensional subset S of R^n we also introduce global versions of this discrete…

We consider the quadractic NLS posed on a bidimensional compact Riemannian manifold $(M, g)$ with $ \partial M \neq \emptyset$. Using bilinear and gradient bilinear Strichartz estimates for Schr\"odinger operators in two-dimensional compact…

We consider the magnetic Ginzburg-Landau equations in a compact manifold $N$ $$ \begin{cases} -\varepsilon^2 \Delta^{A} u=\frac{1}{2}(1-|u|^2)u,\\ \varepsilon^2 d^*dA=\langle\nabla^A u,iu\rangle \end{cases} $$ formally corresponding to the…

Let $f\colon M^{2n}\to\mathbb{R}^{2n+\ell}$, $n \geq 5$, denote a conformal immersion into Euclidean space with codimension $\ell$ of a Kaehler manifold of complex dimension $n$ and free of flat points. For codimensions $\ell=1,2$ we show…

For each cardinal $\kappa$, each natural number $n$ and each simplicial complex $K$ we construct a space $\nu^n_\kappa(K)$ and a map $\pi \colon \nu^n_\kappa(K) \to K$ such that the following conditions are satisfied. 1. $\nu^n_\kappa(K)$…

We show that the space $\text{Lip}_0(\mathbb R^n)$ is the dual space of $L^{1}({\mathbb R}^{n}; {\mathbb R}^{n})/N$ where $N$ is the subspace of $L^{1}({\mathbb R}^{n}; {\mathbb R}^{n})$ consisting of vector fields whose divergence…

Erd\"os proved in 1946 that if a set $E\subset\mathbb{R}^n$ is closed and non-empty, then the set, called ambiguous locus or medial axis, of points in $\mathbb{R}^n$ with the property that the nearest point in $E$ is not unique, can be…

The problem of starlikeness of Teichmuller spaces in Bers' embedding was raised in 1974 and is solved (negatively) for Teichmuller spaces of sufficiently large dimensions. The original proof given by the author relies on the existence of…

This short note describes the tentative form of a finite-dimensional optimization problem that may be of use in a second-generation proof of the Kepler conjecture. In the original 1998 proof of the Kepler conjecture, the form of the…

Let F(X,n):= X^n-\Delta be the complementary of the union \Delta of the diagonals of X^n and let U be a quotient of F(X,n) (possibly trivial) by a subgroup of the symmetric group S_n. We construct compactifications of U in products of…

An n-dimensional analogue of the Klein bottle arose in our study of topological complexity of planar polygon spaces. We determine its integral cohomology algebra and stable homotopy type, and give an explicit immersion and embedding in…

Beben and Wu showed that if $M$ is a $(2n-2)$-connected $(4n-1)$-dimensional Poincar\'{e} Duality complex such that $n\geq 3$ and $H^{2n}(M;\mathbb{Z})$ consists only of odd torsion, then $\Omega M$ can be decomposed up to homotopy as a…

For a cocycle of invertible real $n$-by-$n$ matrices, the Multiplicative Ergodic Theorem gives an Oseledets subspace decomposition of $\mathbb{R}^n$; that is, above each point in the base space, $\mathbb{R}^n$ is written as a direct sum of…

The question, under what geometric assumptions on a space X an n-quasiflat in X implies the existence of an n-flat therein, has been investigated for a long time. It was settled in the affirmative for Busemann spaces by Kleiner, and for…