相关论文: Robust Morphological Measures for Large-Scale Stru…
In this article we carry out a detailed investigation of the geometric nature of the points at infinity of Minkowski superspace. It turns out that there are several sets of points forming the superconformal boundary of Minkowski superspace:…
We study unimodular measures on the space $\mathcal M^d$ of all pointed Riemannian $d$-manifolds. Examples can be constructed from finite volume manifolds, from measured foliations with Riemannian leaves, and from invariant random subgroups…
We investigate the geometric properties of lightlike surfaces in the Minkowski space $\R^{2,1}$, using Cartan's method of moving frames to compute a complete set of local invariants for such surfaces. Using these invariants, we give a…
We discuss here geometric structures of condensed matters by means of a fundamental topological method. Any geometric pattern can be universally represented by a decomposition space of a topological space consisting of the infinite product…
In $\mathbb{R}^n$, we establish an asymptotically sharp upper bound for the upper Minkowski dimension of $k$-porous sets having holes of certain size near every point in $k$ orthogonal directions at all small scales. This bound tends to…
We present an approach to the study of stationary measures placing Tarski's foundational work in this area within a modern category theoretic context. Guiding this work is the notion that measurable spaces equipped with symmetries carry an…
We formulate a general method for perturbative evaluations of statistics of smoothed cosmic fields, and provide useful formulas in application of the perturbation theory to various statistics. This formalism is an extensive generalization…
Decomposition spaces are a class of function spaces constructed out of well-behaved coverings and partitions of unity of a set. The structure of the covering of the set determines the properties of the decomposition space. Besov spaces,…
The normal map given by Birkhoff orthogonality yields extensions of principal, Gaussian and mean curvatures to surfaces immersed in three-dimensional spaces whose geometry is given by an arbitrary norm and which are also called Minkowski…
A wide variety of complex systems are characterized by interactions of different types involving varying numbers of units. Multiplex hypergraphs serve as a tool to describe such structures, capturing distinct types of higher-order…
We establish a Minkowski measurability criterion for a large class of relative fractal drums (or, in short, RFDs), in Euclidean spaces of arbitrary dimension in terms of their complex dimensions, which are defined as the poles of their…
Macroscopic spherical particles spontaneously form rich patterns on a standing Faraday wave. These patterns are found to follow a very systematic trend depending on the floater concentration $\phi$: The same floaters that accumulate at…
We introduce a family of local inhomogeneous mark-weighted summary statistics, of order two and higher, for general marked point processes. Depending on how the involved weight function is specified, these summary statistics capture…
After a brief digression on the current landscape of theoretical physics and on some open questions pertaining to coherence with experimental results, still to be settled, it is shown that the properties of the Deformed Minkowski space lead…
Consider a complex projective space with its Fubini-Study metric. We study certain one parameter deformations of this metric on the complement of an arrangement (=a finite union of hyperplanes) whose Levi-Civita connection is of Dunkl…
We define a class of spaces on which one may generalise the notion of compactness following motivating examples from higher-dimensional number theory. We establish analogues of several well-known topological results (such as Tychonoff's…
Theoretical and observational challenges to standard cosmology such as the cosmological constant problem and tensions between cosmological model parameters inferred from different observations motivate the development and search of new…
In this paper we propose methods for inference of the geometric features of a multivariate density. Our approach uses multiscale tests for the monotonicity of the density at arbitrary points in arbitrary directions. In particular, a…
The topology of an object describes global properties that are insensitive to local perturbations. Classic examples include string knots and the genus (number of handles) of a surface: no manipulation of a closed string short of cutting it…
We consider the corresponding Christoffel-Minkowski problem for curvature measures. The existence of star-shaped $(n-k)$-convex bodies with prescribed $k$-th curvature measures ($k>0$) has been a longstanding problem. This is settled in…