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

We prove (without using Federer's structure theorem) that a finite-mass flat chain over any coefficient group is rectifiable if and only if almost all of its 0-dimensional slices are rectifiable. This implies that every flat chain of finite…

We prove the Aharoni Berger Conjecture

Simple demonstrations based on the equivalence principle are given of how a folded chain and a horizontal flat chain fall down when one chain end is fixed to a rigid support.

In this paper, we proved the normal scalar curvature conjecture and the Bottcher-Wenzel conjecture.

We prove several extensions of the Erdos-Fuchs theorem.

We provide a simple proof for the union-closed sets conjecture, a long-standing open problem in set theory with immediate applications to graph theory, number theory, and order-theory.

We present a streamlined and simplified proof of the Kakeya set conjecture in $\mathbb{R}^3$.

We produce a new, shorter construction of a minor-universal planar graph.

We give a new proof of the existence of designs, which is much shorter and gives better bounds.

A way to obtain the series solutions of the 1 + 2 dimensional continuous Toda chain is presented.

We expose here a short proof of Cramer's theorem in R based on convex duality.

We give a proof of the uniform convergence of Fourier series, using the methods of nonstandard analysis.

We will give a simple proof of the ambiguous class number formula.

A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.

The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…

We give a new short proof of the most simple relation between consecutive power sums of the first m positive integers.

A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case

We present a conjecture about partitions, with a very elementary formulation.

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

We give a simple proof of the Fourier Inversion Theorem, using the methods of nonstandard analysis.