Related papers: A local Mazur-Ulam theorem
These informal notes, not intended for publication, provide an approach to the Borsuk--Ulam theorem via Stokes' theorem, in a similar spirit to Lima's proof of the Brouwer fixed point theorem. They are intended to be accessible to anyone…
The purpose of this paper is to generalize the classical Mazur's lemma from the classical convex analysis to the framework of locally $L^0$-convex modules. In this version an extra condition of countable concatenation is included. We…
We prove Union-Closed sets conjecture.
We present in this work a new and simple proof of the false centre theorem.
In this paper, we provide a concrete interpretation of equivariant Reidemeister torsion and demonstrate that Bismut-Zhang's equivariant Cheeger-M\"{u}ller theorem simplifies considerably when applied to locally symmetric spaces. In a…
We observe that the classical Borsuk-Ulam theorem has an easy generalization to maps from an n-manifold M^n to R^n. We point out a geometric corollary.
We prove an infinitary version of the Brauer-Schur theorem.
We study local existence for the Boltzmann equation near a global Maxwellian.
An equivalent but useful version on the Homological Nerve Theorem is proved.
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
We prove a generalized Fej\'er's theorem for locally compact groups.
Generalizing the known results on graded rings and modules, we formulate and prove the equivariant version of the local duality on schemes with a group action. We also prove an equivariant analogue of Matlis duality.
An technically interesting proof of a known theorem.
We prove a local limit theorem for the Euclidian algorithms ; standard, centred and odd, with any cost function of moderate growth.
In this short note, we extend a local $Tb$ theorem that was proved in \cite{GHO} to a full multilinear local $Tb$ theorem.
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
We present a relative form of the Toponogov comparison theorem.
We prove a local-global principle for twisted flag varieties over a semiglobal field.
The goal of this note is to provide a constructive version of the proof of local structure of etale algebras.
We prove the ACC conjecture for local volumes. Moreover, when the local volume is bounded away from zero, we prove Shokurov's ACC conjecture for minimal log discrepancies.