Related papers: A metric lifting theorem
In this paper, we proved a rigidity theorem of the Hodge metric for concave horizontal slices and a local rigidity theorem for the monodromy representation.
Fixed point results with respect to generalized rational contractive mappings in semi-metric spaces endowed with a directed graph are proved. Some examples are provided to illustrate the results. The obtained results extend, improve and…
In this paper, we introduce a new type of coupled fixed point theorem in partially ordered complete metric space. We give an example to support of our result.
This work provides a short but comprehensible overview of some relevant aspects of metric-affine theories of gravity in relation to the physics and astrophysics of compact objects. We shall highlight the pertinence of this approach to…
Various theorems for the preservation of set-theoretic axioms under forcing are proved, regarding both forcing axioms and axioms true in the Levy-Collapse. These show in particular that certain applications of forcing axioms require to add…
We develop a general framework for working with structured lifting problems, establishing closure and uniqueness properties of their solutions. In a subsequent paper, we apply these results to axiomatize computation rules of cubical type…
The theory of lifting classes and the Reidemeister number of single-valued maps of a finite polyhedron $X$ is extended to $n$-valued maps by replacing liftings to universal covering spaces by liftings with codomain an orbit configuration…
The classical Reifenberg's theorem says that a set which is sufficiently well approximated by planes uniformly at all scales is a topological H\"older manifold. Remarkably, this generalizes to metric spaces, where the approximation by…
The forcing theorem is the most fundamental result about set forcing, stating that the forcing relation for any set forcing is definable and that the truth lemma holds, that is everything that holds in a generic extension is forced by a…
Pastures are a class of field-like algebraic objects which include both partial fields hyperfields and have nice categorical properties. We prove several lift theorems for representations of matroids over pastures, including a…
A ring is rigid if there is no nonzero locally nilpotent derivation on it. In terms of algebraic geometry, a rigid coordinate ring corresponds to an algebraic affine variety which does not allow any nontrivial algebraic additive group…
Using the setting of $G$-metric spaces, common fixed point theorems for four maps satisfying the weakly commuting conditions are obtained for various generalized contractive conditions. Several examples are also presented to show the…
In this paper, we establish a common fixed point theorem for two pairs of occasionally weakly compatible single and set-valued maps satisfying a strict contractive condition in a metric space. Our result extends many results existing in the…
We derive general structure and rigidity theorems for submetries $f: M \to X$, where $M$ is a Riemannian manifold with sectional curvature $\sec M \ge 1$. When applied to a non-trivial Riemannian submersion, it follows that $diam X \leq…
We consider bounded 2-metric spaces satisfying an additional axiom, and show that a contractive mapping has either a fixed point or a fixed line.
A central question in dynamics is whether the topology of a system determines its geometry. This is known as rigidity. Under mild topological conditions rigidity holds for many classical cases, including: Kleinian groups, circle…
Recently many papers on cone metric spaces have been appeared, and main topological properties of such spaces have been obtained. A cone metric space is Hausdorff, and first countable, so the topology of it coincides with a topology induced…
We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of…
This work introduces liftings and their associated Young measures as new tools to study the asymptotic behaviour of sequences of pairs $(u_j,Du_j)j$ for $(u_j)_j \in \mathrm{BV}(\Omega;\mathbb{R}^m)$ under weak* convergence. These tools are…
In this paper, we consider a Borel measurable map of a compact metric space which admits an inducing scheme. Under the finite weighted complexity condition, we establish a thermodynamic formalism for a parameter family of potentials…