Related papers: Caratheodory completeness on the complex plane

We introduce a general notion of covering property, of which many classical definitions are particular instances. Notions of closure under various sorts of convergence, or, more generally, under taking kinds of accumulation points, are…

Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of continuous group homomorphisms are established.

We prove many new cases of a conjecture of Calegari-Emerton describing the qualitative properties of completed cohomology. The heart of our argument is a careful inductive analysis of completed cohomology on the Borel-Serre boundary. As a…

We extend the Global Compactness result by M. Struwe (Math. Z, 1984) to any fractional Sobolev spaces $\dot{H}^s(\Omega)$ for $0<s<N/2$ and $\Omega \subset \mathbb{R}^N$ a bounded domain with smooth boundary. The proof is a simple direct…

First of all, we establish compactness of continuous mappings of the Orlicz--Sobolev classes $W^{1,\varphi}_{\rm loc}$ with the Calderon type condition on $\varphi$ and, in particular, of the Sobolev classes $W^{1,p}_{\rm loc}$ for $p>n-1$…

We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopenka's principle. We prove that the necessary large-cardinal…

Kitchloo and Morava give a strikingly simple picture of elliptic cohomology at the Tate curve by studying a completed version of $S^1$-equivariant $K$-theory for spaces. Several authors (cf [ABG],[KM],[L]) have suggested that an equivariant…

We consider the relation between the c-completion of a Lorentz manifold V and its quotient M = V/G, where G is an isometry group acting freely and properly discontinuously. First, we consider the future causal completion case,…

An improvement of the author's result, proved in 1961, concerning necessary and sufficient conditions for the compactness of an imbedding operator is given.

Cocompactness is a property of embeddings between two Banach spaces, similar to but weaker than compactness, defined relative to some non-compact group of bijective isometries. In presence of a cocompact embedding, bounded sequences (in the…

In the paper "Extensional PERs" by P. Freyd, P. Mulry, G. Rosolini and D. Scott, a category $\mathcal{C}$ of "pointed complete extensional PERs" and computable maps is introduced to provide an instance of an \emph{algebraically compact…

In this work, we prove a compactness theorem on the space of all Hamiltonian stationay Lagrangian submanifolds in a compact symplectic manifold with uniform bounds on area and total extrinsic curvature.

There is proved the sufficiency of several conditions for the removability of singularities of complex-analytic sets in domains of $\mathbb C^n$.

Inspired by some Lorentzian versions of the notion of metric and length space introduced by Kunzinger and S\"amman, and more recently, by M\"uller, and Minguzzi and S\"uhr, we revisit the notion of Lorentzian metric space in order to later…

Hiss and Szczepa\'nski proved in 1991 that the holonomy group of any compact flat Riemannian manifold, of dimension at least two, acts reducibly on the rational span of the Euclidean lattice associated with the manifold via the first…

We give a conceptual proof of the fact that if M is a complete submanifold of a space form, then the maximal integral manifolds of the nullity distribution of its second fundamental form through points of minimal index of nullity are…

We prove several theorems on sigma-bounded and sigma-compact pointsets. We start with a known theorem by Kechris, saying that any lightface \Sigma^1_1 set of the Baire space either is effectively sigma-bounded (that is, covered by a…

In this note we give a detailed proof of certain results on geometry of numbers in the $S$-adic case. These results are well-known to experts, so the aim here is to provide a convenient reference for the people who need to use them.

We define a new class of completions of locally symmetric varieties of type IV which interpolates between the Baily-Borel compactification and Mumford's toric compactifications. An arithmetic arrangement in a locally symmetric variety of…

We prove a $C^0$ a priori estimate on a solution of the quaternionic Calabi problem on an arbitrary compact connected HKT-manifold. This generalizes earlier works where this result was proven under certain extra assumptions on the manifold.