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In this article we describe the formulation of null geodesics as null conformal geodesics and their description in the tractor formalism. A conformal extension theorem through an isotropic singularity is proven by requiring the boundedness…

We consider real isotropic geodesics on manifolds endowed with a pseudoconformal structure and their applications to the theory of lightlike hypersurfaces on such manifolds, the geometry of four-dimensional conformal structures of…

An updated version with a few corrections.

This paper has been withdrawn by the author due to errors and bad formalization.

This paper has been withdrawn by the author due to a mistake in the section 4.

Major changes in Sec. II (with much stronger estimates), minor changes in remaining sections, a new title. Deleted Appendix, added 2 new references.

We present a numerical implementation of the geodesic ray transform and its inversion over functions and solenoidal vector fields on two-dimensional Riemannian manifolds. For each problem, inversion formulas previously derived in…

A modified version of this paper is under process and with a new title and abstract. Hence, this version of the article is completely withdrawn.

This paper has been withdrawn by the author due to its main result being included in cond-mat/0403309 by the same author.

The exposition has been significantly altered, hopefully improved.

Physical reasons suggested in \cite{Ha-Ha} for the \emph{Quantum Gravity Problem} lead us to study \emph{type-changing metrics} on a manifold. The most interesting cases are \emph{Transverse Riemann-Lorentz Manifolds}. Here we study the…

The geodesic ray transform, the mixed ray transform and the transverse ray transform of a tensor field on a manifold can all be seen as what we call mixing ray transforms, compositions of the geodesic ray transform and an invertible linear…

A non-proprietary Mission Concept available for presentation to NASA, providing High Area, High Resolution Imaging Spectroscopy and Timing with Arcmin Angular Resolution Submitted in response to NASA 2011 RFI NNH11ZDA018L 'Concepts for the…

In this paper we consider Yamabe type problem for higher order curvatures on manifolds with totally geodesic boundaries. We prove local gradient and second derivative estimates for solutions to the fully nonlinear elliptic equations…

We consider natural conformal invariants arising from the Gauss-Bonnet formulas on manifolds with boundary, and study conformal deformation problems associated to them. The key technique we used is to derive boundary C^2 estimates directly…

We classify non-reductive four-dimensional homogeneous conformally Einstein manifolds.

In this paper, we consider fully nonlinear equations of Krylov type on Riemannian manifolds with negative curvature which naturally arise in conformal geometry. Moreover, we prove the a priori estimates for solutions to these equations and…

In the paper we discuss three different notions of extremal holomorphic mappings: weak $m$-extremals, $m$-extremals and $m$-complex geodesics. We discuss relations between them in general case and in the special cases of unit ball,…

This paper was withdrawn by the author due to an edition's rights

We comment on the paper \"Uber Extremalprobleme der konformen Geometrie (On extremal problems in conformal geometry) by Teichm\"uller, published in 1941. This paper contains ideas on a wide generalization of his previous work on the…