Related papers: The Marker-Steinhorn Theorem

We prove a variation of Gronwall's lemma.

In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case.

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

A one-line proof of a minimax theorem due to Steinerberger is given.

We will present a new proof of the Gromoll-Grove diameter rigidity theorem.

We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.

In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.

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

We settle in the affirmative the Graham-Sloane conjecture.

A proof is given of Rosenthal's \(\ell_1\) theorem.

We suggest an alternative proof of a theorem due to Lambek and Moser using a perceptible model.

This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.

This is an elementary geometrical proof of Birkhoff theorem. It is hardly important, but the pictures behind are quite nice.

In this note we document a gap in an argument in the above paper, and point to new work in the literature giving a complete proof of the main result.

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.

We do not know whether the main result is true, the proof of theorem 2.1 contains a gap.

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.

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

In this paper, we give a refinement of a theorem by Franks, which answers two questions raised by Kang.

We deal with the distribution of N points placed consecutively around the circle by a fixed angle of a. From the proof of Tony van Ravenstein, we propose a detailed proof of the Steinhaus conjecture whose result is the following: the N…