Related papers: A refined trilinear Kakeya estimate in $\mathbb{R}…

A new refinement of the triangle inequality is presented in normed linear spaces. Moreover, a simple characterization of inner product spaces is obtained by using the skew-angular distance.

We give some estimates of type sup*inf for equation of prescribed scalar curvature type in dimenion 3. As a consequence, we derive an uniqueness type result.

In this paper we give an algorithm to recognize triangulable locally nilpotent derivations in dimension three. In case the given derivation is triangulable, our method produces a coordinate system in which it exhibits a triangular form.

In this paper, we investigate three-term linear relations among theta series of positive-definite integral binary quadratic forms. We extend Schiemann's methods to characterize all possible three-term linear relations among theta series of…

This thesis investigates two problems that are discrete analogues of two harmonic analytic problems which lie in the heart of research in the field. More specifically, we consider discrete analogues of the maximal Kakeya operator conjecture…

We establish an upper estimate for the coefficient of quasiconformal reflection with respect to the boundary of an arbitrary isosceles trapezoid in terms of its geometric parameters; the estimate improve the result obtained in the recent…

Marginally specified models have recently become a popular tool for discrete longitudinal data analysis. Nonetheless, they introduce complex constraint equations and model fitting algorithms. Moreover, there is a lack of available software…

This paper studies the structure of Kakeya sets in $\mathbb{R}^3$. We show that for every Kakeya set $K\subset\mathbb{R}^3$, there exist well-separated scales $0<\delta<\rho\leq 1$ so that the $\delta$ neighborhood of $K$ is almost as large…

We construct a constrained trivariate extension of the univariate normalized B-basis of the vector space of trigonometric polynomials of arbitrary (finite) order n defined on any compact interval [0,\alpha], where \alpha is a fixed (shape)…

Given a triangulation of a closed topological cube, we show that (under some technical condition) there is an essentially unique tiling of a rectangular parallelepiped by cubes, indexed by the vertices of the triangulation. Moreover, i -…

Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings. As a consequence, one obtains bounds for…

We prove sharp Strichartz-type estimates in three dimensions, including some which hold in reverse spacetime norms, for the wave equation with potential. These results are also tied to maximal operator estimates studied by…

In this short note, we treat an unbalanced shifted convolution sum of Fourier coefficients of cusp forms by a rather simple argument. Our result improves previous results established by more advanced approaches.

We study some properties convex functions fulfill. Among the conclusions we obtain from such result, we are able to prove some nontrivial inequalities among real numbers, and we give an improvement of the reverse triangle inequality in the…

We present a complete system of inequalities for the inradius, circumradius, and diameter in the $3$-dimensional Euclidean space. To do so, we prove quasiconcavity of the inradius evaluated over $n$-simplices with a common facet…

Extension dimension is characterized in terms of $\omega$-maps. We apply this result to prove that extension dimension is preserved by refinable maps between metrizable spaces. It is also shown that refinable maps preserve some…

Let $X$ be a compact K{\"a}hler manifold of dimension three. We prove that there exists a projective manifold $Y$ such that $\pi\_1(X)\simeq \pi\_1(Y)$. We also prove the bimeromorphic existence of algebraic approximations for compact…

We examine a family of three-dimensional exponential sums with monomials and provide estimates which are in some instances sharper than those stemming from approaches entailing the use of existing bounds pertaining to analogous sums.

We derive a priori interior Hessian estimates for special Lagrangian equation with critical and supercritical phases in general higher dimensions. Our unified approach leads to sharper estimates even for the previously known three…

In this note we discuss three notions of dimension for triangulated categories: Rouquier dimension, diagonal dimension and Serre dimension. We prove some basic properties of these dimensions, compare them and discuss open problems.