Related papers: Sphere theorems for RCD and stratified spaces
First, we review the basic mathematical structures and results concerning the gauge orbit space stratification. This includes general properties of the gauge group action, fibre bundle structures induced by this action, basic properties of…
General equations of the unified field theory, obtained using the curved and torsional space-time, are presented. They contain only independent geometrical parameters (metric and connections) of the metric-affine space, and describe the…
In this work, we study topological properties of surface bundles, with an emphasis on surface bundles with a spin structure. We develop a criterion to decide whether a given manifold bundle has a spin structure and specialize it to surface…
Spherically symmetric static empty space solutions are studied in f(R) theories of gravity. We reduce the set of modified Einstein's equations to a single equation and show how one can construct exact solutions in different f(R) models. In…
In this paper, we derive a Riccati-type equation applicable to (sub-)static Einstein spaces and examine its various applications. Specifically, within the framework of conformally compactifiable manifolds, we prove a splitting theorem for…
The spherical Radon transform on the unit sphere can be regarded as a member of the analytic family of suitably normalized generalized cosine transforms. We derive new formulas for these transforms and apply them to study classes of…
Astrophysical bounds on the cosmological constant are examined for spherically symmetric bodies. Similar limits emerge from hydrostatical and gravitational equilibrium and the validity of the Newtonian limit. It is argued that the bound…
We study algebraic varieties parametrized by topological spaces and enlarge the domains of Lawson homology and morphic cohomology to this category. We prove a Lawson suspension theorem and splitting theorem. A version of Friedlander-Lawson…
We prove fixed point theorems in a space with a distance function that takes values in a partially ordered monoid. On the one hand, such an approach allows one to generalize some fixed point theorems in a broad class of spaces, including…
We study exact solutions of the Einstein-Maxwell equations for the interior gravitational field of static spherically symmetric charged compact spheres. The spheres consist of an anisotropic fluid with a charge distribution that gives rise…
The universal perturbative invariants of rational homology spheres can be extracted from the Chern-Simons partition function by combining perturbative and nonperturbative results. We spell out the general procedure to compute these…
In this thesis four separate problems in general relativity are considered, divided into two separate themes: coordinate conditions and perfect fluid spheres. Regarding coordinate conditions we present a pedagogical discussion of how the…
We study semantic and syntactic properties of spherical orders and their elementary theories, including finite and dense orders and their theories. It is shown that theories of dense $n$-spherical orders are countably categorical and…
In the present paper we consider the Einstein-multiple-scalar field theory. When the target space of the scalar fields is a complete, simply connected Riemannian manifold with non-positive sectional curvature we prove that the static and…
The Ernst equation is formulated on an arbitrary Riemann surface. Analytically, the problem reduces to finding solutions of the ordinary Ernst equation which are periodic along the symmetry axis. The family of (punctured) Riemann surfaces…
Derrick's theorem is an important result that decides the existence of soliton configurations in field theories in different dimensions. It is proved using the extremization of finite energy of configurations under the scaling…
In this paper we consider generalizations of classical results on chains of tangent spheres to higher dimensions.
In this paper, Clairaut's theorem is expressed on the surfaces of rotation in semi Euclidean 4-space. Moreover, the general equations of time-like geodesic curves are characterized according to the results of Clairaut's theorem on the…
We provide a set of general tools to study the problem of stellar equilibrium in any gravitational theory in which spherically symmetric spacetimes satisfy master field equations taking the form of an equality between an identically…
We show that in the Snyder space the area of the disc and of the sphere can be quantized. It is also shown that the area spectrum of the sphere can be related to the Bekenstein conjecture for the area spectrum of a black hole horizon.