Related papers: A short note on Godbersen's Conjecture

This is a short addendum to a note of Beauville on the subject of the title. We prove an inequality that takes into account the constant part of the Jacobian.

We present new bounds for the Berezin number inequalities which improve on the existing bounds. We also obtain bounds for the Berezin norm of operators as well as the sum of two operators.

We give a lower bound on the probability of error in quantum state discrimination. The bound is a weighted sum of the pairwise fidelities of the states to be distinguished.

The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…

The Hodge conjecture is shown to be equivalent to a question about the homology of very ample divisors with ordinary double point singularities. The infinitesimal version of the result is also discussed.

In this paper, we will continue the investigation of Waring's problem, and give further improvements.

The aim of this short note is to extend the recent variational proof of partial regularity for optimal transport maps to the case of continuous densities.

We collect a few guesses on possible implications of a lower bound on the scalar curvature of a Riemannian manifold on the size and shape of this manifold.

Newtonian limit of Extended Theories of Gravity (in particular, higher--order and scalar--tensor theories) is theoretically discussed taking into account recent observational and experimental results.

We investigate additive properties of sets $A,$ where $A=\{a_1,a_2,\ldots ,a_k\}$ is a monotone increasing set of real numbers, and the differences of consecutive elements are all distinct. It is known that $|A+B|\geq c|A||B|^{1/2}$ for any…

The Simes inequality has received considerable attention recently because of its close connection to some important multiple hypothesis testing procedures. We revisit in this article an old result on this inequality to clarify and…

We report the results of our empirical investigations on the Bateman-Horn conjecture. This conjecture, in its commonly known form, produces rather large deviations when the polynomials involved are not monic. We propose a modified version…

We give a new lower bound for the essential minimum of subvarieties of abelian varieties with small codimension, under a conjecture about ordinary primes in abelian varieties. This lower bound is already known in the toric case since the…

We survey recent developments towards a proof of the Penrose conjecture and results on Penrose-type and other geometric inequalities for quasi-local masses in general relativity.

We consider the problem of lower bounding a generalized Minkowski measure of subsets of a convex body with a log-concave probability measure, conditioned on the set size. A bound is given in terms of diameter and set size, which is sharp…

We prove that finite perimeter subsets of $\mathbb{R}^{n+1}$ with small isoperimetric deficit have boundary Hausdorff-close to a sphere up to a subset of small measure. We also refine this closeness under some additional a priori integral…

A solution is given to a conjecture proposed by Y. Wigderson and A. Wigderson concerning a "Heisenberg-like" uncertainty principle. This is an old article already published in 2022.

We make two tiny corrections to our previous paper with the same title, and also obtain, as a bonus, something new.

We establish some qualitative properties of minimizers in the fractional Hardy--Sobolev inequalities of arbitrary order.

We prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the Trotter-Kato theorem for contraction semigroups. From this theorem, general results on the convergence of approximations…