Related papers: A local Mazur-Ulam theorem

A short proof of the Mazur-Ulam theorem concerning isometries of real normed spaces.

We revise a proof of a Mazur-Ulam theorem for generalized gyrovector spaces.

A rephrasing of Vogt's and Skof's version of the Ulam-Mazur theorem as a definability statement.

We give a revision of the proof of a Mazur-Ulam theorem for generalized gyrovector spaces given in the paper "Generalized gyrovector spaces and a Mazur-Ulam theorem" published in Publ. Math. Debrecen, 87 (2015), 393--413.

In this paper we present a Kakutani type theorem that is equivalent to the Borsuk--Ulam theorem for manifolds.

We derive extensions of the monomialization theorems for morphisms of varieties in our earlier work. In this note we show that a local monomialization can be found which satisfies stronger local conditions. Some comments are made about how…

The classical Mazur--Ulam theorem which states that every surjective isometry between real normed spaces is affine is not valid for non-Archimedean normed spaces. In this paper, we establish a Mazur--Ulam theorem in the non-Archimedean…

The classical Mazur-Ulam theorem establishes that every surjective isometry between normed real vector spaces is an affine transformation. In various applied mathematical settings, however, one encounters maps that preserve distances not…

We intoduce a local version of the Jordan-Brouwer separation theorem and deduce some global statements, some of which may follow from known results, but the technique is new.

We give a sufficient condition for the local limit theorem. To construct it, we employ infinite times of convolutions of probability density functions.

We give a new proof of Lucas' Theorem in elementary number theory.

The main result of this paper is that in order to prove the local uniformization theorem for local rings it is enough to prove it for rank one valuations. Our proof does not depend on the nature of the class of local rings for which we want…

We prove a Borel version of the local lemma, i.e. we show that, under suitable assumptions, if the set of variables in the local lemma has a structure of a Borel space, then there exists a satisfying assignment which is a Borel function.…

The local H theorem is shown to hold for the Enskog equation with a modified Enskog factor proposed by the authors [Phys. Rev. E 111, 065108 (2025)]. This is a stronger statement than the global one in the same paper and has been obtained…

We prove a variation of Gronwall's lemma.

We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.

We prove several extensions of the Erdos-Fuchs theorem.

The decomposition theorem is deduced from local purity.

In this paper we give an elementary proof of the local sum conjecture in two dimensions. In a remarkable paper [CMN, arXiv:1810.11340], this conjecture has been established in all dimensions using sophisticated, powerful techniques from a…

A new proof of the decomposition theorem is established using a relation with a version of the local purity theorem of Deligne and Gabber adapted to complex algebraic varieties.