Related papers: A norm - inequality related to affine regular hexa…

We determine those norms on B(H) whose unit ball is C*-convex. We call them M-norms and show that the class of M-norms less than a given norm enjoys a maximum element. These minimum and maximum elements will be determined in some cases.…

It is a classical fact in Euclidean geometry that the regular polygon maximizes area amongst polygons of the same perimeter and number of sides, and the analogue of this in non-Euclidean geometries has long been a folklore result. In this…

A double-normal pair of a finite set $S$ of points from Euclidean space is a pair of points $\{p,q\}$ from $S$ such that $S$ lies in the closed strip bounded by the hyperplanes through $p$ and $q$ that are perpendicular to $pq$. A…

We show that the minimum distance projection in the L1-norm from an interior point onto the boundary of a convex set is achieved by a single, unidimensional projection. Application of this characterization when the convex set is a…

The aim of this paper is to investigate the differential geometry of immersed surfaces in three-dimensional normed spaces from the viewpoint of affine differential geometry. We endow the surface with a useful Riemannian metric which is…

A recent paper showed how to find sets of finite affine or projective planes constructed on a common set of points, so that lines of one plane meet lines of a different plane in at most two points. In this paper, those results are…

The present work concerns spherical spin glass models with disorder satisfying a uniform logarithmic Sobolev inequality. We show that the Hessian descent algorithm introduced by Subag can be extended to this setting, thanks to the abundance…

Let X be a real or complex Hilbert space of finite but large dimension d, let S(X) denote the unit sphere of X, and let u denote the normalized uniform measure on S(X). For a finite subset B of S(X), we may test whether it is approximately…

Given a finite sequence $a:={a_1, ..., a_N}$ in a domain $\Omega \subset C^n$, and complex scalars $v:={v_1, ..., v_N}$, consider the classical extremal problem of finding the smallest uniform norm of a holomorphic function verifying…

Let $\Delta_m$ be the standard $m$-dimensional simplex of non-negative $m+1$ tuples that sum to unity and let $S$ be a nonempty subset of $\Delta_m$. A real valued function $h$ defined on a convex subset of a real vector space is $S$-almost…

Let $S$ be a set of $n$ points in the plane, $\wp(S)$ be the set of all simple polygons crossing $S$, $\gamma_P$ be the maximum angle of polygon $P \in \wp(S)$ and $\theta =min_{P\in\wp(S)} \gamma_P$. In this paper, we prove that…

Conditional on Fourier restriction estimates for elliptic hypersurfaces, we prove optimal restriction estimates for polynomial hypersurfaces of revolution for which the defining polynomial has non-negative coefficients. In particular, we…

Gradients of the perimeter and area of a polygon have straightforward geometric interpretations. The use of optimality conditions for constrained problems and basic ideas in triangle geometry show that polygons with prescribed area…

We introduce a similarity relation between submodules of a module $M$ over a ring $R$, extending the classical notion of similarity for right ideals. Focusing on (faithfully) projective modules, we establish a sharp lower bound for the…

We introduce a new family of affine metrics on a locally strictly convex surface $M$ in affine 4-space. Then, we define the symmetric and antisymmetric equiaffine planes associated with each metric. We show that if $M$ is immersed in a…

In this paper, we develop approximation error estimates as well as corresponding inverse inequalities for B-splines of maximum smoothness, where both the function to be approximated and the approximation error are measured in standard…

Inspired by the boolean discrepancy problem, we study the following optimization problem which we term \textsc{Spherical Discrepancy}: given $m$ unit vectors $v_1, \dots, v_m$, find another unit vector $x$ that minimizes $\max_i \langle x,…

Let $V$ be a finite dimensional inner product space over $\mathbb{R}$ with dimension $n$, where $n\in \mathbb{N}$, $\wedge^{r}V$ be the exterior algebra of $V$, the problem is to find $\max_{\| \xi \| = 1, \| \eta \| = 1}\| \xi \wedge \eta…

We prove the regularity of cohomogeneity two equivariant isotopy minimization problems. Based on this, we develop cohomogeneity two equivariant min-max theory for minimal hypersurfaces proposed by Pitts and Rubinstein in 1988. As an…

A planar point set is in convex position precisely when it has a convex polygonization, that is, a polygonization with maximum interior angle measure at most \pi. We can thus talk about the convexity of a set of points in terms of the…