Related papers: A variation of Gronwall's lemma
We obtain simple proofs of certain inequalites for bivariate means.
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 give a short and self-contained proof of Levi's Extension Lemma for pseudoline arrangements.
We prove a result on the existence of linear forms of a given Diophantine type.
The proof, but not the statement, of Proposition 18.2 contained an error which is repaired in this version. See Remark 18.3 in this version. No other changes. We extend Greenberg's original construction to arbitrary (in particular,…
We present a relative form of the Toponogov comparison theorem.
We present a rough path analog of the classical Gronwall Lemma introduced recently by A. Deya, M. Gubinelli, M. Hofmanov\'a, S. Tindel in [arXiv:1604.00437] and discuss two of its applications. First, it is applied in the framework of rough…
We improve constants in the Rademacher-Menchov inequality.
It is shown that the formula for the variance of combined series yields surprisingly simple proofs of some well known variance bounds.
We give an elementary short proof of Grothendieck's base change theorem for the cohomology of flat coherent sheaves.
Gronwall conjecture states that a planar 3-web which admits more than one distinct linearization is locally equivalent to an algebraic web. We give a partial answer to the conjecture in the affirmative for the class of planar 3-webs with…
We study a variant of algebraic K-theory and prove that it is stable and preserves module structures.
We prove a version for mixed groups for a Fuchs' result about connections between the cancellation property of a group and the unit lifting property of its (Walk-)endomorphism rings.
We give a new proof of the existence of designs, which is much shorter and gives better bounds.
Error in proof of theorem 10.
We prove a Tannakian form of Drinfeld's lemma for isocrystals on a variety over a finite field, equipped with actions of partial Frobenius operators. This provides an intermediate step towards transferring V. Lafforgue's work on the…
We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].
We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.
An observation on Hall-Littlewood polynomials.
We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.