Related papers: A relative Toponogov comparison theorem

An algebraic deformation theory of coalgebra morphisms is constructed.

We establish a relative version of Gromov's Vanishing Theorem in the presence of amenable open covers with small multiplicity, extending a result of Li, L\"oh, and Moraschini. Our approach relies on Gromov's theory of multicomplexes.

In this paper we prove a relative index theorem for pairs of generalized Dirac operators on orbifolds which are the same at infinity. This generalizes to orbifolds a celebrated theorem of Gromov and Lawson.

We prove several extensions of the Erdos-Fuchs theorem.

We give a simple proof of the existence of a minimizer for the Sobolev inequality. Our proof is based on a representation formula via a cut-off fundamental solution.

An observation on Hall-Littlewood polynomials.

In this article we discuss a generalized Wirtinger inequality.

In this paper, we introduce a family of topological spaces that captures the existence of preservation theorems. The structure of those spaces allows us to study the relativisation of preservation theorems under suitable definitions of…

We prove a local version of the Mazur-Ulam theorem.

This is a short survey of amenable equivalence relations.

In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.

In this note, we will consider an arithmetic analogue of Bogomolov unstability theorem.

An introduction to circle valued Morse theory and Novikov homology, from an algebraic point of view.

In this short paper we review and extract some features of the Fredholm Alternative problem .

We give a simple proof of Dorronsoro's theorem and use similar ideas to establish an equivalence for embeddings of vector fields.

We survey some basic results on the Gromov-Prohorov distance between metric measure spaces. (We do not claim any new results.) We give several different definitions and show the equivalence of them. We also show that convergence in the…

By using the properties of the uniformly distributed sequences of real numbers on $(0,1)$, a short proof of a certain version of Kolmogorov strong law of large numbers is presented which essentially differs from Kolmogorov's original proof.

We present a short and self-contained proof of the choosability version of Brooks' theorem.

We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.

In this note, we demonstrate the convergence of the Demailly approximation of a general (weakly) upper semi-continuous weight.