Related papers: Conformal Scalar Curvature Equations in Open Space…
In this paper, we study the existence of constant holomorphic d-scalar curvature and the prescribing holomorphic d-scalar curvature problem on closed, connected almost Hermitian manifolds of dimension $n\geq6$. In addition, we obtain an…
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…
Second order partial differential equations which describe spherical surfaces (ss) or pseudospherical surfaces (pss) are considered. These equations are equivalent to the structure equations of a metric with Gaussian curvature $K = 1$ or $K…
We point out how some recent developments in the theory of constant scalar curvature K\"ahler metrics can be used to clarify the existence issue for such metrics in the special case of geometrically ruled complex surfaces.
We focus on studying, numerically, the scalar curvature tensor in a two-dimensional discrete space. The continuous metric of a two-sphere is transformed into that of a lattice using two possible slicings. In the first, we use two integers,…
We study the Yamabe problem on open manifolds of bounded geometry and show that under suitable assumptions there exist Yamabe metrics, i.e. conformal metrics of constant scalar curvature. For that, we use weighted Sobolev embeddings.
The divergences coming from a particular sector of gravitational fluctuations around a generic background in general theories of quadratic gravity are analyzed. They can be summarized in a particular type of scalar model, whose properties…
A nonstationary spherically symmetric problem for conformal geometrodynamics equations is considered and general exact solutions in quadratures are obtained. Involvement of Weyl degrees of freedom allows us to consider the problem with…
This paper constructs continuously self-similar solution of a spherically symmetric gravitational collapse of a scalar field in n dimensions. The qualitative behavior of these solutions is explained, and closed-form answers are provided…
We consider the problem of finding a metric in a given conformal class with prescribed nonpositive scalar curvature and nonpositive boundary mean curvature on a compact manifold with boundary, and establish a necessary and sufficient…
In this paper some open problems for Painlev\'e equations are discussed. In particular the following open problems are described: (i) the Painlev\'e equivalence problem; (ii) notation for solutions of the Painlev\'e equations; (iii)…
We give a metric characterization of the scalar curvature of a smooth Riemannian manifold, analyzing the maximal distance between $(n+1)$ points in infinitesimally small neighborhoods of a point. Since this characterization is purely in…
We give an overview of the existence and regularity results for curvature flows and how these flows can be used to solve some problems in geometry and physics.
We study some conformally invariant integral equations using the method of moving spheres.
Given a conformal metric with finite total Q-curvature, we show that the assumptions on scalar curvature sensitively govern the Q-curvature integral. Additionally, we introduce a conformal mass for such manifolds. Using such mass, we…
We construct all orthogonal separating coordinates in constant curvature spaces of arbitrary signature. Further, we construct explicit transformation between orthogonal separating and flat or generalised flat coordinates, as well as…
In this paper, we study the interior gradient estimates for admissible solutions to prescribed curvature equations in hyperbolic space.
We show that conformal blocks simplify greatly when there is a large difference between two of the scaling dimensions for external operators. In particular the spacetime dimension only appears in an overall constant which we determine via…
Conformal fields are a recently discovered class of representations of the algebra of vector fields in $N$ dimensions. Invariant first-order differential operators (exterior derivatives) for conformal fields are constructed.
The full causal ladder of spacetimes is constructed, and their updated main properties are developed. Old concepts and alternative definitions of each level of the ladder are revisited, with emphasis in minimum hypotheses. The implications…