Related papers: Conformal Scalar Curvature Equations in Open Space…
We formulate several conjectures on mean convex domains in the Euclidean spaces, as well as in more general spaces with lower bonds on their scalar curvatures, and prove a few theorems motivating these conjectures.
The classification problem for conformally-flat space-times that admit a separation of variables in the Hamilton-Jacobi equation of the scalar-tensor Brans-Dicke theory of gravity is examined. The field equations of the scalar-tensor theory…
In this paper, we establish the curvature estimates for a class of Hessian type equations. Some applications are also discussed.
In entanglement computations for a free scalar field with coupling to background curvature, there is a boundary term in the modular Hamiltonian which must be correctly specified in order to get sensible results. We focus here on the…
We describe conformal field theories, correlation functions of which satisfy equations of the two-dimensional fluid mechanics. Prediction for the energy spectrum is given, $E(k) \sim k^{-25/7}$.
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
The soft topological spaces and some their related concepts have stud- ied in [7]. In this paper, we introduce and study the notions of soft connected topological spaces after a review of preliminary definitions.
The trace anomaly for a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary is considered. In the context of a perturbative evaluation of the theory's effective action explicit…
The dynamics of cosmic scalar fields with flat potential is studied. Their contribution to the expansion rate of the universe is analyzed, and their behaviour in a simple model of phase transitions is discussed.
We show that results about spaces or moduli spaces of positive scalar curvature metrics proved using index theory can typically be extended to non-negative scalar curvature metrics. We illustrate this by providing explicit generalizations…
From higher dimensional theories, e.g. string theory, one expects the presence of non-minimally coupled scalar fields. We review the notion of conformal frames in cosmology and emphasize their physical equivalence, which holds at least at a…
A class of curves with special conformal properties (conformal curves) is studied on the Reissner-Nordstr\"om spacetime. It is shown that initial data for the conformal curves can be prescribed so that the resulting congruence of curves…
We compute curvature-dependent graviton correlation functions and couplings as well as the full curvature potential $f(R)$ in asymptotically safe quantum gravity coupled to scalars. The setup is based on a systematic vertex expansion about…
We derive a formula for the curvature tensor of the natural Riemannian metric on the space of two-dimensional conformal field theories and also a formula for the curvature tensor of the space of boundary conformal field theories.
Projective structures on curves appear naturally in many areas of mathematics, from extrinsic conformal geometry to analysis, where the main problem is to find qualitative information about the solutions of Hill equations. In this paper, we…
The problem of conformal transformation and conformal flatness of Finsler spaces has been studied by so many researchers $\left[ 6,16,17,20,21\right] .$ Recently, Prasad et. al $\left[ 19\right] $ have studied three dimensional conformally…
The "conformal mass prescriptions" were used recently to calculate the mass of spacetimes in higher dimensional and higher curvature theories of gravity. These definitions are closely related to Komar integrals for spacetimes that are…
In this paper we establish the existence in low dimensions of solutions to the constraint equations in the case of the conformal system recently proposed by David Maxwell, with the added presence of a scalar field and under suitable…
This is a review of two-dimensional conformal field theory including some of the relations to integrable models. An effort is made to develop the basic formalism in a way which is as elementary and flexible as possible at the same time.…
Within recently proposed scenario which explains flatness of the spectrum of scalar cosmological perturbations by a combination of conformal and global symmetries, we discuss the effect of weak breaking of conformal invariance. We find that…