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A natural extension of Riemannian geometry to a much wider context is presented on the basis of the iterated differential form formalism developed in math.DG/0605113 and an application to general relativity is given.

We survey recent advances in the theory of graph and hypergraph decompositions, with a focus on extremal results involving minimum degree conditions. We also collect a number of intriguing open problems, and formulate new ones.

Conformal electrodynamics is a particularly interesting example of power Maxwell non-linear electrodynamics, designed to possess conformal symmetry in all dimensions. In this paper, we propose a regularized version of Conformal…

This paper has excessive overlap with the following papers also written by the authors or their collaborators: gr-qc/0207026, gr-qc/0502059, gr-qc/0502061, and gr-qc/0510038.

This paper is withdrawn. A revised and expanded version of this work is available as hep-ph/9603323.

In this paper, partly based on Zachos' PhD thesis, we show that the geodesic X-ray transform is stably invertible near infinity on a class of asymptotically conic manifolds which includes perturbations of Euclidean space. In particular…

We study weighted simultaneous rational approximation to points of the form $(1,\xi,\xi^2)$, for a class of extremal real numbers $\xi$, within the framework of multi-parametric geometry of numbers.

Let M be a smooth complex projective variety and let L be a line bundle on it. Rays-positive manifolds, namely pairs (M,L) such that L is numerically effective and L\cdotR > 0 for all extremal rays R on M, are studied. Several illustrative…

This paper is a review of recent and classical results on integrable geodesic flows on Riemannian manifolds and topological obstructions to integrability. We also discuss some open problems.

This article surveys recent results aiming at obtaining refined mapping estimates for the X-ray transform on a Riemannian manifold with boundary, which leverage the condition that the boundary be strictly geodesically convex. These…

%auto-ignore This paper has been withdrawn by the author. The attribution of hard spectral features of x-ray novae to neutron star surfaces and gap accretion was incorrect.

In this work, we study the existence and nonexistence of solution for strongly coupled elliptic systems to m-parameters.

In this paper, we systematically investigate the geometry and topology of manifolds with integral radial curvature bounds, and obtain many interesting and important conclusions.

We propose a new reconstruction method for scalar--tensor gravity based on the use of conformal transformations. The new method allows the derivation of a set of interesting exact cosmological solutions in brans Dicke gravity as well as…

The aim of the present paper is to investigate conformal changes in absolute parallelism geometry. We find out some new conformal invariants in terms of the Weitzenb\"ock connection and the Levi-Civita connection of an absolute parallelism…

We provide a commentary on Teichm{\"u}ller's paper "Extremale quasikonforme Abbildungen und quadratische Differentiale" (Extremal quasiconformal mappings of closed oriented Riemann surfaces), Abh. Preuss. Akad. Wiss., Math.-Naturw. Kl.…

This paper has been withdrawn by the corresponding author because the newest version is now published in Discrete Applied Mathematics.

This paper has been withdrawn in order to replace it by two separate submissions: 1. Hamiltonian 2-forms in Kahler geometry III: Extremal metrics and stability, math.DG/0511118; 2. Hamiltonian 2-forms in Kahler geometry IV: Weakly…

We complete the classification of almost commutative geometries from a particle physics point of view given in hep-th/0312276. Four missing Krajewski diagrams will be presented after a short introduction into irreducible, non-degenerate…

This paper has been withdrawn because of serious errors.