Related papers: Generalized $\alpha$-attractor models from element…
Using noncommutative geometry, the standard tools of differential geometry can be extended to a broad class of spaces whose coordinates are noncommuting operators acting on a Hilbert space. In the simplest case of coordinates being matrix…
We assign some kind of invariant manifolds to a given integrable PDE (its discrete or semi-discrete variant). First, we linearize the equation around its arbitrary solution $u$. Then we construct a differential (respectively, difference)…
The Standard Model of elementary particle physics is one of the most successful models of contemporary theoretical physics being in full agreement with experiments. However, its mathematical structure deserves further investigations both…
Cosmological $\alpha$-attractors stand out as particularly compelling models to describe inflation in the very early universe, naturally meeting tight observational bounds from cosmic microwave background (CMB) experiments. We investigate…
It is known that besides the usual unitary mappings $\Omega = 1/\Omega^\dagger$ between the equivalent representations of the physical Hilbert space of Quantum Mechanics (often, Fourier transformations), the generalized non-unitary maps…
Generalizing both hyperbolic framed surfaces and one-parameter families of hyperbolic framed curves, we introduce the concept of hyperbolic generalized framed surfaces and establish their relations in hyperbolic 3-space. We provide the…
In this paper, we consider the contracting curvature flow of smooth closed surfaces in $3$-dimensional hyperbolic space and in $3$-dimensional sphere. In the hyperbolic case, we show that if the initial surface $M_0$ has positive scalar…
It is known that the fairly (most?) general class of 2D superintegrable systems defined on 2D spaces of constant curvature and separating in (geodesic) polar coordinates is specified by two types of radial potentials (oscillator or…
This paper investigates the geometry of canonically polarized surfaces defined over a field of positive characteristic which have a nontrivial global vector field, and the implications that the existence of such surfaces has in the moduli…
We consider the familiar problem of a minimally coupled scalar field with quadratic potential in flat Friedmann-Lema\^itre-Robertson-Walker cosmology to illustrate a number of techniques and tools, which can be applied to a wide range of…
The dynamics of any spherical cosmology with a scalar field (`scalaron') coupling to gravity is described by the nonlinear second-order differential equations for two metric functions and the scalaron depending on the `time' parameter. The…
We show that there is a mildly nonlinear three-dimensional system of ordinary differential equations - realizable by a rather simple electronic circuit - capable of producing a generalized attracting horseshoe map. A system specifically…
We establish the well-posedness of a strongly damped semilinear wave equation equipped with nonlinear hyperbolic dynamic boundary conditions. Results are carried out with the presence of a parameter distinguishing whether the underlying…
We investigate the Hilbert complex of elasticity involving spaces of symmetric tensor fields. For the involved tensor fields and operators we show closed ranges, Friedrichs/Poincare type estimates, Helmholtz type decompositions, regular…
We consider certain universal functors on symmetric quotient stacks of Abelian varieties. In dimension two, we discover a family of $\mathbb{P}$-functors which induce new derived autoequivalences of Hilbert schemes of points on Abelian…
We prove generalizations of the isoperimetric inequality for both spherical and hyperbolic wave fronts (i.e. piecewise smooth curves which may have cusps). We then discuss "bicycle curves" using the generalized isoperimetric inequalities.…
Aleksandrov surfaces are a generalization of two-dimensional Riemannian manifolds, and it is known that every open simply connected Aleksandrov surface is conformally equivalent either to the unit disc (hyperbolic case) or to the plane…
We consider a generalization of the notion of spaces of homogeneous type, inspired by recent work of Street [21] on the multi-parameter Carnot-Caratheodory geometry, which imbues such spaces with differentiability structure. The setting…
We systematically study the preinflationary dynamics of the spatially flat Friedmann-Lemaitre-Robertson-Walker universe filled with a single scalar field that has the generalized $\alpha-$attractor potentials, in the framework of loop…
We survey the distributional properties of progressively dilating sets under projection by covering maps, focusing on manifolds of constant sectional curvature. In the Euclidean case, we review previously known results and formulate some…