相关论文: Enriched Riemann Sphere, Morse Stability and Equi-…
Based on an earlier introduced new class of generalized gravity-matter models defined in terms of two independent non-Riemannian volume forms (alternative generally covariant integration measure densities) on the space-time manifold, we…
In this paper we investigate Cauchy completeness and exponentiablity for quantale enriched categories, paying particular attention to probabilistic metric spaces.
We consider endomorphisms of a compact manifold which are expanding except for a finite number of points and prove the existence and uniqueness of a physical measure and its stochastical stability. We also characterize the zero-noise limit…
In "The Yang-Mills equations over Riemann surfaces", Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory. We generalize their study to all closed, compact, connected, possibly…
On the basis of our recent modifications of the Dirac formalism we generalize the Bargmann-Wigner formalism for higher spins to be compatible with other formalisms for bosons. Relations with dual electrodynamics, with the…
We consider families of transformations in multidimensional Riemannian manifolds with non-uniformly expanding behavior. We give sufficient conditions for the continuous variation (in the $L^1$-norm) of the densities of absolutely continuous…
We revisit the problem of the deformed oscillator with position-dependent mass [da Costa et al., J. Math. Phys. {\bf 62}, 092101 (2021)] in the classical and quantum formalisms, by introducing the effect of the mass function in both kinetic…
Given the unital C$^*$-algebra $A$, the unitary orbit of the projector $p_0=\begin{pmatrix}1 & 0 \\ 0 & 0 \end{pmatrix}$ in the C$^*$-algebra $M_2(A)$ of $2\times 2$ matrices with coefficients in $A$ is called in this paper, the Riemann…
We considered an extension of the standard functional for the Einstein-Dirac equation where the Dirac operator is replaced by the square of the Dirac operator and a real parameter controlling the length of spinors is introduced. For one…
In this article the algebra and the basis of corresponding analysis in 4-dimensional spaces are constructed, in pseudoeuclidean with signature (1, -1, -1, -1) and pseudo-Riemannian corresponding to the real space-time. In both cases the…
For a complete Riemannian manifold $M$ with an (1,1)-elliptic Codazzi self-adjoint tensor field $A$ on it, we use the divergence type operator ${L_A}(u): = div(A\nabla u)$ and an extension of the Ricci tensor to extend some major comparison…
Our objective is to develop a stratified Morse theory with tangential conditions. We define a continuous strata-wise smooth Morse function on an abstract stratified space by using control conditions and radiality assumptions on the gradient…
In the framework of the Einstein-Dirac-aether theory the extended model is established, in which the backreaction of the spinor field on the unit vector field, describing the dynamic aether, is taken into account. For this purpose, we…
We prove several quantitative stability estimates for solutions of complex Monge-Ampere equations when both the cohomology class and the prescribed singularity vary. In a broad sense, our results fit well into the study of degeneration of…
Let $M$ be a smooth, compact, connected, oriented Riemannian manifold, and let $\imath: M \to \mathbb R^d$ be an isometric embedding. We show that a Sobolev map $f: M \to M$ which has the property that the differential $df(q)$ is close to…
For the tensor field of rank-2 there are two unitary irreducible representation (UIR) in de Sitter (dS) space denoted by $\Pi^{\pm}_{2,2}$ and $\Pi^{\pm}_{2,1}$ [1]. In the flat limit only the $\Pi^{\pm}_{2,2}$ coincides to the UIR of…
In this note we discuss the geometry of Riemannian surfaces having a discrete set of singular points. We assume the conformal structure extends through the singularities and the curvature is integrable. Such points are called \emph{simple…
We study the motion of neutral and charged spinning bodies in curved space-time in the test-particle limit. We construct equations of motion using a closed covariant Poisson-Dirac bracket formulation which allows for different choices of…
We evaluate a one-loop, two-point, massless Feynman integral $I_{D,m}(p,q)$ relevant for perturbative field theoretic calculations in strongly anisotropic $d=D+m$ dimensional spaces given by the direct sum $\mathbb R^D\oplus\mathbb R^m$.…
The existence and stability of the Einstein static solution have been built in the Einstein-Cartan gravity. We show that this solution in the presence of perfect fluid with spin density satisfying the Weyssenhoff restriction is cyclically…