Related papers: The general dual-polar Orlicz-Minkowski problem
A problem of Glasner, now known as Glasner's problem, asks whether every minimally almost periodic, monothetic, Polish groups is extremely amenable. The purpose of this short note is to observe that a positive answer is obtained under the…
We consider a class of doubly nonlinear degenerate hyperbolic-parabolic equations with homogeneous Dirichlet boundary conditions, for which we first establish the existence and uniqueness of entropy solutions. We then turn to the…
In this paper, we deal with the successive inner and outer radii with respect to Orlicz Minkowski sum. The upper and lower bounds for the radii of the Orlicz Minkowski sum of two convex bodies are established.
In this short survey we want to present some of the impact of Minkowski's successive minima within Convex and Discrete Geometry. Originally related to the volume of an $o$-symmetric convex body, we point out relations of the successive…
We introduce and investigate the notion of a `generalized equation' of the form $f(D^2 u)=0$, based on the notions of subequations and Dirichlet duality. Precisely, a subset ${{\mathbb H}}\subset {\rm Sym}^2({\mathbb R}^n)$ is a generalized…
Goal of the presented research is to construct simplified model of the core-halo structures in binary systems. Examples are provided by Thorne-Zytkov objects, hot Jupiters, protoplanets with large moons, red supergiants in binaries and…
We describe a post-Minkowskii approximation of general relativity as a power series expansion in G, Newton's gravitational constant. Material sources are hidden behind boundaries, and only the vacuum Einstein equations are considered. An…
In this paper, given a prescribed measure on $\mathbb{S}^1$ whose density is bounded and positive, we establish a uniform diameter estimate for solutions to the planar $L_p$ dual Minkowski problem when $0<p<1$ and $q\ge 2$. We also prove…
We describe the formalism to compute gravitational-wave observables for compact binaries via the effective field theory framework in combination with modern tools from collider physics. We put particular emphasis on solving the "multi-loop"…
The two-body problem in General Relativity has been the subject of many analytical investigations. After reviewing some of the methods used to tackle this problem (and, more generally, the N-body problem), we focus on a new, recently…
Multiple orthogonality is considered in the realm of a Gauss--Borel factorization problem for a semi-infinite moment matrix. Perfect combinations of weights and a finite Borel measure are constructed in terms of M-Nikishin systems. These…
We prove that the Cauchy problem for the Chern-Simons-Higgs equations on the (2+1)-dimensional Minkowski space-time is globally well posed for initial data with finite energy. This improves a result of Chae and Choe, who proved global…
The aim of this note is to describe the computation of post-Minkwoskian Hamiltonians in modified theories of gravity. Exploiting a recent relation between amplitudes of massive scalars and Hamiltonians for relativistic point-particles, we…
We search for vortices in a generalized Abelian Chern-Simons model with a nonstandard kinetic term. We illustrate our results, plotting and comparing several features of the vortex solution of the generalized model with those of the vortex…
In this paper, we introduce the concept of N-dimensional generalized Minkowski space, i.e. a space endowed with a (in general non-diagonal) metric tensor, whose coefficients do depend on a set of non-metrical coodinates. This is the first…
We study the Lorentzian Calder\'on problem, where the objective is to determine a globally hyperbolic Lorentzian metric up to a boundary fixing diffeomorphism from boundary measurements given by the hyperbolic Dirichlet-to-Neumann map. This…
This paper explores the nonuniqueness of solutions to the $L_p$ chord Minkowski problem for negative $p.$ The $L_p$ chord Minkowski problem was recently posed by Lutwak, Xi, Yang and Zhang, which seeks to determine the necessary and…
In this paper, we study two-dimensional steady solitary gravity waves propagating along the surface of a fluid of finite depth. In particular, we can deal with general vorticity distributions and overhanging wave profiles. By conformal…
We study the precise asymptotic volume of balls in Orlicz spaces and show that the volume of the intersection of two Orlicz balls undergoes a phase transition when the dimension of the ambient space tends to infinity. This generalizes a…
To be observed and analyzed by the network of current gravitational wave detectors (LIGO, Virgo, KAGRA), and in anticipation of future third generation ground based (Einstein Telescope, Cosmic Explorer) and space borne (LISA) detectors,…