Related papers: Another simple proof of the 1-dimensional flat cha…

We give a new, elementary proof of the fact that metric 1-currents in the Euclidean space correspond to Federer-Fleming flat chains.

Proofs that a smooth morphism is flat available in the literature are long and difficult. We give a short proof of this fact.

We propose a simple model which possesses the chain fountain effect.

This survey summarizes recent progress on the flat chain conjecture, which asserts the equivalence between metric currents and flat chains with finite mass in the Euclidean space. In particular, we focus on recent work showing that the…

In this note, we provide a short proof of Feige's conjecture for identically distributed random variables.

Here is present short proofing of Jordan's theorem about dividing of flat on two disjoint subsets by one closed curve.

We give a short and relatively elementary proof of the Hilton-Milner Theorem.

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

We prove Union-Closed sets conjecture.

We give a one-sentence elementary proof of the combinatorial Fa\`a di Bruno's formula.

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

A proof of Sendov's conjecture is given.

Here we outline a proof for the 4-dimensional smooth Poincare Conjecture.

We prove a flat strip theorem for 2-dimensional ptolemaic spaces.

I present a simple derivation of the de Gennes narrowing phenomenon.

In this note we give a short, direct proof of the well known Combinatorial Nullstellensatz.

The purpose of the paper is to present an short proof of the Chuang's inequality.

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.