Related papers: A short proof of the irreflexivity conjecture

We present a much simplified proof of Dehn's theorem on the infinitesimal rigidity of convex polytopes. Our approach is based on the ideas of Trushkina and Schramm.

The incompressibility method is an elementary yet powerful proof technique. It has been used successfully in many areas. To further demonstrate its power and elegance we exhibit new simple proofs using the incompressibility method.

The article provides a counterexample to a conjecture by Blocki-Zwonek.

A short proof to a recent theorem of Giambruno and Mishchenko is given in this note.

We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.

In this note a far extension of the Banach fixed point theorem is proved.

A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.

We give a new proof of the $L^2$ version of Hardy's uncertainty principle based on calculus and on its dynamical version for the heat equation. The reasonings rely on new log-convexity properties and the derivation of optimal Gaussian decay…

We prove a recent conjecture of Sean A. Irvine about a nonlinear recurrence, using mechanized guessing and verification. The theorem-prover Walnut plays a large role in the proof.

In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.

We give a relatively short and self contained proof of Ratner's theorem in the special case of SL(2,R)-invariant measures.

We give a short proof of Ahlfors' theorem on covering surfaces.

We give for the first time a detailed proof of the Palamodov's total instability conjecture in Lagrangian dynamics. This proves an older related Lyapunov instability conjecture posed by Lyapunov and Arnold and reduces the Lagrange-Dirichlet…

We develop a family of simple rank one theories built over quite arbitrary sequences of finite hypergraphs. (This extends an idea from the recent proof that Keisler's order has continuum many classes, however, the construction does not…

We give a new proof of the reversibility of the Schramm Loewner evolution for $\kappa \leq 4$. The main ideas used in the proof are similar to those used in the original proof of this result, given by Zhan.

Motivated by the variations of Sarnak's conjecture due to El Abdalaoui, Kulaga-Przymus, Lemanczyk, De La Rue and by the observation that the Mobius function is a good weight (with limit zero) for the polynomial pointwise ergodic theorem in…

This note contains a newly streamlined version of the original proof that Outer space is contractible.

This note presents an especially short and direct variant of Hermite's proof of the simple continued fraction expansion e = [2,1,2,1,1,4,1,1,6,...] and explains some of the motivation behind it.

In this paper, we prove a conjecture of Schnell in the surface case.

A very simple but useful almost sure convergence theorem of probability is given.