Related papers: Weighted algebraic topology, II (Real valued metri…
Mostly aimed at an audience with backgrounds in geometry and homological algebra, these notes offer an introduction to derived geometry based on a lecture course given by the second author. The focus is on derived algebraic geometry, mainly…
We discuss class of doubled geometry models with diagonal metrics. Based on the analysis of known examples we formulate a hypothesis that supports treating them as modified bimetric gravity theories. Certain steps towards the generic case…
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…
Motivated by properties of higher tangent lifts of geometric structures, we introduce concepts of weighted structures for various geometric objects on a manifold F equipped with a homogeneity structure. The latter is a smooth action on F of…
Geodesic metric spaces support a variety of averaging constructions for given finite sets. Computing such averages has generated extensive interest in diverse disciplines. Here we consider the inverse problem of recognizing computationally…
In this paper, we endow the right half plane with warped product metrics. The group of holomorphic isometries of all such metrics is isomorphic to the real additive group. Of our interest are two of those metrics: they have zero and…
We present a thorough study of the differential geometry of weightings and develop the theory of weightings for vector bundles, Lie groupoids, and Lie algebroids. We begin by extending the work of Loizides and Meinrenken on weighted…
This is the second of two works concerning the Sobolev calculus on metric measure spaces and its applications. In this work, we focus on several approaches to vector calculus in the non-smooth setting of complete and separable metric spaces…
In this paper we construct a wavelet basis in weighted L^2 of Euclidean space possessing vanishing moments of a fixed order for a general locally finite positive Borel measure. The approach is based on a clever construction of Alpert in the…
We prove trace theorems for weighted mixed norm Sobolev spaces in the upper-half space where the weight is a power function of the vertical variable. The results show the differentiability order of the trace functions depends only on the…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
Network theory provides a rich toolbox consisting of methods, measures, and models for studying the structure and dynamics of complex systems found in nature, society, or technology. Recently, it has been pointed out that many real-world…
In a previous paper, the general approach for treatment of algebraic equations of different order in gravity theory was exposed, based on the important distinction between covariant and contravariant metric tensor components. In the present…
In the first part of this investigation, [Ha], we generalized a weighted distance function of [Li] and found necessary and sufficient conditions for it being a metric. In this paper some properties of this so-called M-relative metric are…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
This is the second of a series of papers studying real algebraic threefolds using the minimal model program. The main result is the following. Let $X$ be a smooth projective real algebraic 3-fold. Assume that the set of real points is an…
In recent contributions, algebraic multigrid methods have been designed and studied from the viewpoint of the spectral complementarity. In this note we focus our efforts on specific applications and, more precisely, on large linear systems…
This article presents a novel mathematical formalism for advanced manifold--metric pairs, enhancing the frameworks of geometry and topology. We construct various D-dimensional manifolds and their associated metric spaces using functional…
We investigate metric projections and distance functions referring to convex bodies in finite-dimensional normed spaces. For this purpose we identify the vector space with its dual space by using, instead of the usual identification via the…
Magnitude and (co)weightings are quite general constructions in enriched categories, yet they have been developed almost exclusively in the context of Lawvere metric spaces. We construct a meaningful notion of magnitude for flow graphs…