Related papers: A direct approach to the anisotropic Plateau probl…
We investigate Whitehead's asphericity question from a new perspective, using results and techniques of the homotopy theory of finite topological spaces. We also introduce a method of reduction to investigate asphericity based on the…
This paper constructs two immediate extensions of the existing anisotropic solutions in the context of Einstein-Maxwell framework by employing minimal geometric deformation. To achieve this, we assume a static spherical interior initially…
We prove compactness of solutions of a fully nonlinear Yamabe problem satisfying a lower Ricci curvature bound, when the manifold is not conformally diffeomorphic to the standard sphere. This allows us to prove the existence of solutions…
Minimum Riesz energy problems in the presence of an external field are analyzed for a condenser with touching plates. We obtain sufficient and/or necessary conditions for the solvability of these problems in both the unconstrained and the…
This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…
The paper investigates various $p$-adic versions of Littlewood's conjecture, generalizing a set-up considered recently by de Mathan and Teulie. In many cases it is shown that the sets of exceptions to these conjectures have Hausdorff…
Fitzpatrick's variational representation of maximal monotone operators is here extended to a class of pseudo-monotone operators in Banach spaces. On this basis, the initial-value problem associated with the first-order flow of such an…
The following well known open problem is answered in the negative: Given two compact spaces $X$ and $Y$ that admit minimal homeomorphisms, must the Cartesian product $X\times Y$ admit a minimal homeomorphism as well? A key element of our…
This thesis is devoted to the study of well-posedness properties of some geometric variational problems: existence, regularity and uniqueness of solutions. We study two specific problems arising in the context of geometric calculus of…
We obtain a class of anisotropic spherically symmetric relativistic solutions of compact objects in hydrostatic equilibrium in the $f(R,T) =R+2\chi T$ modified gravity, where $R$ is the Ricci scalar, $T$ is the trace of the energy momentum…
Simple generic extensions of isotropic Durgapal--Fuloria stars to the anisotropic domain are presented. These anisotropic solutions are obtained by guided minimal deformations over a self gravitating isotropic system. When the isotropic and…
In the first part of this article, we complete the program announced in the preliminary note [8] by proving a conjecture presented in [9] that states the equivalence of contractibility and p_{1}-stability for generalized spaces of formal…
This work comprises a detailed theoretical and computational study of the boundary value problem for transversely isotropic linear elastic bodies. General conditions for well-posedness are derived in terms of the material parameters. The…
We investigate the approximation of Monge--Kantorovich problems on general compact metric spaces, showing that optimal values, plans and maps can be effectively approximated via a fully discrete method. First we approximate optimal values…
In this paper, we develop a new class of models for a compact star with anisotropic stresses inside the matter distribution. By assuming a linear equation of state for the anisotropic matter composition of the star we solve the Einstein…
In this paper, we have introduced new viable solutions of Einstein-Maxwell field equations by incorporating the features of anisotropic matter distribution in the realm of General theory of Relativity ($GR$). For this procurement, we have…
In this brief note we show that under a volume non-preserving scaling it is possible to recover the basics for a regularity theory regarding local weak solutions to a parabolic fully anisotropic equation. We characterize self-similar…
This paper presents new approaches to the fixed point property for nonexpansive mappings in L^1 spaces. While it is well-known that L^1 fails the fixed point property in general, we provide a complete and self-contained proof that…
We demonstrate a technique to generate new class of exact solutions to the Einstein-Maxwell system describing a static spherically symmetric relativistic star with anisotropic matter distribution. An interesting feature of the new class of…
We consider minimal submanifolds of negatively curved spaces with small curvature. We show that in a Hadamard space with negatively pinched curvature $-C\leq K\leq -1$, complete minimal submanifolds with second fundamental form less than…