相关论文: A Short Proof of the Poincar\'e Conjecture

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

We prove an effective version of the Oppenheim conjecture with a polynomial error rate. The proof is based on an effective equidistribution theorem which in turn relies on recent progress towards restricted projection problem.

We describe two distinct simple, short and self contained proofs of the composition lemma.

In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.

In a recent talk of Robbert Fokkink, some conjectures related to the infinite Tribonacci word were stated by the speaker and the audience. In this note we show how to prove (or disprove) the claims easily in a "purely mechanical" fashion,…

This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.

We give a new proof of a_4\phi_3 summation due to G.E. Andrews and confirm another_4\phi_3 summation conjectured by him recently. Some variations of these two_4\phi_3 summations are also given.

We give a new simpler proof of a theorem of Jayne and Rogers.

We present some reflections concerning two papers by H. Poincar\'e concerning the theory of quanta.

In the paper are proved theorems, which amplify the results of my paper "On the difference equation of Poincare type (Part 3)", Max-Plank-Institut fuer Mathematik, Bonn, Preprint Series, 2004, 09, 1-34.

In this paper we state some conjectures about q-Fibonacci polynomials which for q=1 reduce to well-known results about Fibonacci numbers and Fibonacci polynomials.

A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.

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

In this short note we present a family of counterexamples to the King's conjecture.

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

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

We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…

In this short exposition we provide a simplified proof of Buser's result for Cheeger's isoperimetric constant.

We find a new proof for the celebrated theorem of Keith and Zhong that a $(1,p)$-Poincar\'e inequality self-improves to a $(1,p-\epsilon)$-Poincar\'e inequality. The paper consists of a novel characterization of Poincar\'e inequalities and…

This note gives a new elementary proof of Poincar\'e-Miranda theorem based on Sard's theorem and the simple classification of one-dimensional manifolds.