Related papers: Extreme Geometric Quantiles Under Minimal Assumpti…
On the base of the distinction between covariant and contravariant metric tensor components, an approach from algebraic geometry will be proposed, aimed at finding new solutions of the Einstein's equations both in GTCCCM and in standard…
The aim of this paper is to investigate extremum problems with pay-off being the total variational distance metric defined on the space of probability measures, subject to linear functional constraints on the space of probability measures,…
We extend the formulation of gauged supergravity in five dimensions, as obtained by compactification of $M$~theory on a deformed Calabi-Yau manifold, to include non-universal matter hypermultiplets. Even in the presence of this gauging,…
We classify maximal totally geodesic submanifolds in exceptional symmetric spaces up to isometry. Moreover, we introduce an invariant for certain totally geodesic embeddings of semisimple symmetric spaces, which we call the Dynkin index. We…
We generalize the concept of extremal index of a stationary random sequence to the series scheme of identically distributed random variables with random series sizes tending to infinity in probability. We introduce new extremal indices…
In this paper we provide a connection between the geometrical properties of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the…
We classify the allowed structures of the discrete 1-form gauge sector in six-dimensional supergravity theories realized as F-theory compactifications. This provides upper bounds on the 1-form gauge factors $\mathbb{Z}_m$ and in particular…
We here conjecture that two much-studied aspects of quantum gravity, dimensional flow and spacetime fuzziness, might be deeply connected. We illustrate the mechanism, providing first evidence in support of our conjecture, by working within…
In this paper, a noncommutative gravitational theory is constructed by applying Moyal deformation quantization and the Seiberg-Witten map to teleparallel gravity, a classical gravitational theory, as a gauge theory of local translational…
The Hamiltonian for dynamic geometry generates the evolution of a spatial region along a vector field. It includes a boundary term which determines both the value of the Hamiltonian and the boundary conditions. The value gives the…
We study the existence of cubic quotients of finite-dimensional quasi-normed spaces, that is, quotients well isomorphic to $\ell_{\infty}^k$ for some $k.$ We give two results of this nature. The first guarantees a proportional dimensional…
Non-extremal black holes are endowed with geometric invariants related to their horizon areas. We extend earlier work on hot attractor black holes to higher dimensions and add a scalar potential. In addition to the event and Cauchy…
Black holes exist all over our Universe, possessing a very wide range of masses. At the moment, they serve as a probe to test general relativity at astrophysical scales, but in the future they may also give us information about gravity at…
Several important measures of quantum correlations of a state of a finite-dimensional composite system are defined as linear combinations of marginal entropies of this state. This paper is devoted to the infinite-dimensional generalizations…
Associated to every stationary extremal black hole is a unique near-horizon geometry, itself a solution of the field equations. These latter spacetimes are more tractable to analyze and most importantly, retain properties of the original…
The theory of embedded random surfaces, equivalent to two--dimensional quantum gravity coupled to matter, is reviewed, further developed and partly generalized to four dimensions. It is shown that the action of the Liouville field theory…
This paper deals with the subject of infinitesimal variations of Euclidean submanifolds with arbitrary dimension and codimension. The main goal is to establish a Fundamental theorem for these geometric objects. Similar to the theory of…
A universal relation between the leading correction to the entropy and extremality was gotten in the work of Goon and Penco. In this paper, we extend this work to the massive gravity and investigate thermodynamic extremality relations in a…
This paper develops a notion of geometric quantiles on Hadamard spaces, also known as global non-positive curvature spaces. After providing some definitions and basic properties, including scaled isometry equivariance and a necessary…
We apply recently developed convex programs to find the minimal-area Riemannian metric on $2n$-sided polygons ($n\geq 3$) with length conditions on curves joining opposite sides. We argue that the Riemannian extremal metric coincides with…