Related papers: The Minimal Euclidean Function on the Gaussian Int…

This paper establishes three minimax theorems for possibly nonconvex functions on Euclidean spaces or on infinite-dimensional Hilbert spaces. The theorems also guarantee the existence of saddle points. As a by-product, a complete solution…

Denote by $E_\epsilon$ the Ginzburg-Landau functional in the plane and let $\tilde u_\varepsilon$ be the radial solution to the Euler equation associated to the problem $\min \left\{E_\varepsilon(u,B_1): \>\left. u\right\vert _{\partial…

This paper gives, in generic situations, a complete classification of ruled minimal surfaces in pseudo-Euclidean space with arbitrary index. In addition, we discuss the condition for ruled minimal surfaces to exist, and give a…

A new method for approximating fractional derivatives of the Gaussian function and Dawson's integral are presented. Unlike previous approaches, which are dominantly based on some discretization of Riemann-Liouville integral using polynomial…

Variational calculations using Gaussian wave functionals combined with an approximate projection on gauge invariant states are presented. We find that the energy exhibits a minimum for a wave functional centered around a non vanishing…

In this note we present techniques to compute inhomogeneous minima of norm forms; as an application, we determine all norm-Euclidean complex bicyclic quartic number fields.

In this paper we study a group theoretical generalization of the well-known Gauss's formula that uses the generalized Euler's totient function introduced in [11].

This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…

Entropy functionals (i.e. convex integral functionals) and extensions of these functionals are minimized on convex sets. This paper is aimed at reducing as much as possible the assumptions on the constraint set. Dual equalities and…

The main goal of this paper is to provide a group theoretical generalization of the well-known Euler's totient function. This determines an interesting class of finite groups.

On any metric space, I provide an intrinsic characterization of those complex-valued functions which are uniform limits of Lipschitz functions. There are applications to function theory on complete Riemannian manifolds and, in particular,…

We prove the ACC for minimal log discrepancies on an arbitrary fixed threefold.

We consider the fundamental task of optimising a real-valued function defined in a potentially high-dimensional Euclidean space, such as the loss function in many machine-learning tasks or the logarithm of the probability distribution in…

Euler calculus is based on integrating simple functions with respect to the Euler characteristic. This paper makes the case for extending Euler calculus to continuous integrands by integrating with respect to (Gaussian) curvature. This…

Let $Z$ be an $n$-dimensional Gaussian vector and let $f: \mathbb R^n \to \mathbb R$ be a convex function. We show that: $$\mathbb P \left( f(Z) \leq \mathbb E f(Z) -t\sqrt{ {\rm Var} f(Z)} \right) \leq \exp(-ct^2),$$ for all $t>1$, where…

Let $G$ be a nonempty bounded domain in a finite-dimensional Euclidean space. The main results are general estimates from below at points from $G$ for an arbitrary subharmonic function $u\not\equiv -\infty$ on the closure of the domain $G$…

A surprising simple result about quadrilaterals is given as an application of the vector triple product identity.

In this paper we study the everywhere H\"oder continuity of the minima of a class of vectorial integral funcionals

We consider the Gaussian curvature conjecture of a minimal graph $S$ over the unit disk. First of all we reduce the general conjecture to the estimating the Gaussian curvature of some Scherk's type minimal surfaces over a quadrilateral…

In this thesis, we study value distribution theoretical properties of the Gauss map of pseudo-algebraic minimal surfaces in n-dimensional Euclidean space. After reviewing basic facts, we give estimates for the number of exceptional values…