Related papers: Huber Theorem revisited in dimensions 2 and 4

A regularization procedure, that allows one to relate singularities of curvature to those of the Einstein tensor without some of the shortcomings of previous approaches, is proposed. This regularization is obtained by requiring that (i) the…

In this note, we show that several self-dual spacetimes previously studied in the context of celestial and twisted holography arise as limits of a certain Taub-NUT AdS$_4$ metric, the Pedersen metric, in which their Mass, NUT charge and…

This is the second of two works concerning the Sobolev calculus on metric measure spaces and its applications. In this work, we focus on several approaches to vector calculus in the non-smooth setting of complete and separable metric spaces…

In the first part Busemann concavity as non-negative curvature is introduced and a bi-Lipschitz splitting theorem is shown. Furthermore, if the Hausdorff measure of a Busemann concave space is non-trivial then the space is doubling and…

We set up an Einstein-Gauss-Bonnet theory in four dimensions, based on the recent formulation of pure gravity with extra dimensions of vanishing metrical length [1]. In absence of torsion, the effective field equations depend only on the…

Seminar held at JINR, Dubna, May 15, 2012. In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities - with smooth but degenerate metric - which,…

In this paper, we prove that a two-dimensional self-shrinker, homeomorphic to the sphere, immersed in the three dimensional Euclidean space is a round sphere, provided its mean curvature and the norm of its position vector have an upper…

Einstein-Gauss-Bonnet gravity in five-dimensional spacetime provides an excellent example of a theory that, while including higher-order curvature corrections to General Relativity, still shares many of its features, such as second-order…

Deformations of gauged WZW actions are constructed for any pair $(G,H)$ by taking different embeddings of the gauge group $H\subset G$ as it acts on the left and right of the group element $g$. This leads to models that are dual to each…

We construct two dimensional gauge theories with $N= (4,4)$ supersymmetry from branes of type IIA string theory. Quantum effects in the two dimensional gauge theory are analyzed by embedding the IIA brane construction into M-theory. We find…

In this article, we propose the following conjecture: if the Strominger connection of a compact Hermitian manifold has constant non-zero holomorphic sectional curvature, then the Hermitian metric must be K\"ahler. The main result of this…

We extend the structure theory of Burago--Gromov--Perelman for Alexandrov spaces with curvature bounded below, to the setting of Busemann spaces with non-negative curvature. We prove that any finite-dimensional Busemann space with…

Let $M$ be a closed complex submanifold in ${\mathbb C}^N$ with the complete K\"ahler metric induced by the Euclidean metric. Several finiteness theorems on the $L^p$ Bergman space of holomorphic sections of a given Hermitian line bundle…

Given a compact constant scalar curvature Kaehler orbifold, with nontrivial holomorphic vector fields, whose singularities admit a local ALE Kaehler Ricci-flat resolution, we find sufficient conditions on the position of the singular points…

Using Seiberg-Witten theory, it is shown that any Kaehler metric of constant negative scalar curvature on a compact 4-manifold M minimizes the L^2-norm of scalar curvature among Riemannian metrics compatible with a fixed decomposition…

Using a combination of techniques from conformal and complex geometry, we show the potentialization of 4-dimensional closed Einstein-Weyl structures which are half-algebraically special and admit a "half-integrable" almost-complex…

We consider the question of how the doubling characteristic of a measure determines the regularity of its support. The question was considered by David, Kenig, and Toro for codimension-1 under a crucial assumption of flatness, and later by…

We study static black holes in quadratic gravity with planar and hyperbolic symmetry and non-extremal horizons. We obtain a solution in terms of an infinite power-series expansion around the horizon, which is characterized by two…

In this paper we consider the existence and regularity problem for Coulomb frames in the normal bundle of two-dimensional surfaces with higher codimension in Euclidean spaces. While the case of two codimensions can be approached directly by…

The conformal gravity is one of the most important models of quantum gravity with higher derivatives. We investigate the role of the Gauss-Bonnet term in this theory. The coincidence limit of the second coefficient of the Schwinger-DeWitt…