Related papers: A simple case within Nash-Moser-Ekeland theory

We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological type. We also provide a discussion of the assumptions, and an…

We give an elementary proof of the reducedness of twisted loop groups along the lines of the Kneser-Tits problem.

In this paper, we prove a fine condensation theorem. This is quite similar to condensation theorems for pure extender mice in the literature, except that condensation for iteration strategies has been added to the mix.

We derive an interesting congruence relation motivated by an Indian Olympiad problem. We give three different proofs of the theorem and mention a few interesting related results.

We give an elementary and constructive proof for a theorem of de Smit et Lenstra. Note: In version 1, was missing the proof that "completely secant" implies "1-secant"

We give a proof of the o-minimal version of the Whitney Extension Theorem simplified as compared to the original ones. A new simplifying ingredient is a definable variant of Urysohn's lemma for class $\mathcal{C}^q$ (see Section 3).

We present a new family of sharp examples for the Szemer\'edi-Trotter theorem. These are the first examples not based on a rectangular lattice. We also include an application to the discrete inverse Loomis-Whitney problem.

We prove the exactness of the Nisnevich Gersten complex over a base under some conditions. We also obtain, as a consequence, a Nisnevich analogue of the Bloch-Ogus theorem for \'{e}tale cohomology in this setting.

In this paper we give an elementary proof for Bertrand's postulate also known as Bertrand-Chebyshev theorem.

We prove an analytic generalization of Koll\'ar's vanishing theorem, which contains the Nadel vanishing theorem as a special case.

In this article we prove a theorem of Ohsawa-Takegoshi type on compact K\"ahler manifolds. Our arguments follow the "standard" approach for this kind of extension results; however, there are many complications arising from the…

We complete statement and proof for B. Moss\'e's unilateral recognizability theorem. We also provide an algorithm for deciding the unilateral non-recognizability of a given primitive substitution.

Based on M. Hall's theorem we prove a simple result dealing with real numbers which admit exact approximations by rationals.

We provide new sufficient conditions under which Ryser's conjecture holds.

In this paper, we present a short proof of Halin's grid theorem.

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

We give a geometric approach to proving know regularity and existence theorems for the 2D Navier-Stokes Equations. We feel this point of view is instructive in better understanding the dynamics. The technique is inspired by constructions in…

In this note, we give a simple proof that the Riemann Hypothesis is unprovable in any reasonable axiom system.

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