International Journal of Mathematics

We extend the Funk–Radon–Helgason inversion method of mean value operators to the Radon transform of continuous and L^p functions which are integrated over matrix planes in the space of real rectangular matrices. Necessary and sufficient conditions of existence of for such f and explicit inversion formulas are obtained. New higher-rank phenomena related to this setting are investigated.

We formulate and prove the Lorentzian version of the positive mass theorems with arbitrary negative cosmological constant for asymptotically AdS spacetimes. This work is the continuation of the second author's recent work on the positive mass theorem on asymptotically hyperbolic 3-manifolds.

We study the formal normal form of a non-integrable almost complex structure. We do this in terms of the vector fields associated to the almost complex structure. We show that locally such a formal normal form exists and we prove a partial convergence result.

Recently, we introduced a description of knots and links in S³ in terms of integral matrices. The purpose of this paper is to show that the delta-unknotting numbers of the knots described by integral matrices with nonzero even entries coincide with the absolute values of the second coefficients of the Conway polynomials of the knots, and give an explicit formula for determining the delta-unknotting numbers of such knots.

The moduli space of G-bundles on an elliptic curve with additional flag structure admits a Poisson structure. The bivector can be defined using double loop group, loop group and sheaf cohomology constructions. We investigate the links between these methods and for the case SL₂ perform explicit computations, describing the bracket and its leaves in detail.