Related papers: A necessary condition for the logarithmic Minkowks…
In the case of symmetries with respect to n independent linear hyperplanes, a stability version of the logarithmic Brunn-Minkowski inequality and the logarithmic Minkowski inequality for convex bodies is established.
In this paper, we solve the $L_p$ chord Minkowski problem in the case of discrete measures whose supports are in general position for negative $p$ and $q>0.$ As for general Borel measure with a density, we also give a proof but need…
Under study are some vector optimization problems over the space of Minkowski balls, i.e., symmetric convex compact subsets in Euclidean space. A typical problem requires to achieve the best result in the presence of conflicting goals;…
Minkowski space serves as a framework for the theoretical constructions that deal with manifestations of relativistic effects in physical phenomena. But neither Minkowski himself nor the subsequent developers of the relativity theory have…
In this paper, we present a new necessary and sufficient condition for which the supremum exists with respect to the logic order. Moreover, we give out a new and much simpler representation of the supremum with respect to the order, our…
We prove a gluing theorem for linearised vacuum gravitational fields in Bondi gauge on a class of characteristic hypersurfaces in static vacuum $(n+1)$-dimensional backgrounds with cosmological constant $ \Lambda \in \mathbb{R}$, $n\ge 4$.…
In this paper, we study the $L_p$-Gaussian Minkowski problem, which arises in the $L_p$-Brunn-Minkowski theory in Gaussian probability space. We use Aleksandrov's variational method with Lagrange multipliers to prove the existence of the…
We consider the Cauchy problem for quadratic nonlinear Klein-Gordon systems in two space dimensions with masses satisfying the resonance relation. Under the null condition in the sense of J.-M. Delort, D. Fang, R. Xue (2004), we show the…
The purpose of this article is to introduce and motivate the notion of Minkowski (or box) dimension for measures. The definition is simple and fills a gap in the existing literature on the dimension theory of measures. As the terminology…
We give necessary integral conditions and sufficient ones for the existence of a general concept of $\mu$-dichotomy for evolution operators defined on the half-line which includes as particular cases the well-known concepts of nonuniform…
Classical bosonic open string models in fourdimensional Minkowski spacetime are discussed. A special attention is paid to the choice of edge conditions, which can follow consistently from the action principle. We consider lagrangians that…
In this paper, we analyze optimal control problems governed by semilinear parabolic equations. Box constraints for the controls are imposed and the cost functional involves the state and possibly a sparsity-promoting term, but not a…
In this paper, we study the $L_p$ dual Minkowski problem for all $q, p \in \mathbb{R}$ from an algebraic perspective. We establish the existence of solutions for group-invariant convex bodies (not necessarily origin-symmetric), thereby…
We note that some form of the condition "$p_1, p_2$ have a $\leq_{\mathbb{Q}}$-lub in $\mathbb{Q}$" is necessary in some forcing axiom for $\lambda$-complete $\mu^+$-c.c. forcing notions. We also show some versions are really stronger than…
Recently, the duals of Federer's curvature measures, called dual curvature measures, were discovered by Huang, Lutwak, Yang, and Zhang (ACTA, 2016). In the same paper, they posed the dual Minkowski problem, the characterization problem for…
Mixed-moment models, introduced before for one space dimension, are a modification of the method of moments applied to a (linear) kinetic equation, by choosing mixtures of different partial moments. They are well-suited to handle such…
We prove the stability of the Einstein-scalar field Lichnerowicz equation under subcritical perturbations of the critical nonlinearity in dimensions 3, 4 and 5. As a consequence, we obtain the existence of a second solution to the equation…
We investigate the Fermat-Torricelli problem in d-dimensional real normed spaces or Minkowski spaces, mainly for d=2. Our approach is to study the Fermat-Torricelli locus in a geometric way. We present many new results, as well as give an…
This paper investigates the \emph{massive} Maxwell-Dirac system under the Lorenz gauge condition in (4+1) dimensional Minkowski space. The focus is on establishing global existence and scattering results for small solutions on the weighted…
We present four-dimensional gauge theories in Minkowski spacetime which effectively generate in certain energy regimes five-dimensional warped geometries whereas, in general, the fifth dimension is latticized. After discussing in detail…