Prescriptive unitarity with elliptic leading singularities

Leading singularities and off-shell conformal integrals

The three-loop four-point function of stress-tensor multiplets in N = 4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In this paper we evaluate the unknown integrals, thus obtaining the three-loop correlation function analytically. The integrals have the generic structure of rational functions multiplied by ...

Hardy-Sobolev Critical Elliptic Equations with Boundary Singularities

Unlike the non-singular case s = 0, or the case when 0 belongs to the interior of a domain Ω in IR(n ≥ 3), we show that the value and the attainability of the best Hardy-Sobolev constant on a smooth domain Ω, μs(Ω) := inf {

Existence of Critical Elliptic Systems with Boundary Singularities

Degenerations of elliptic curves and cusp singularities

This paper gives more or less explicit equations for all twodimensional cusp singularities of embedding dimension at least 4. They are closely related to Felix Klein’s equations for universal curves with level n structure. The main technical result is a description of the versal deformation of an n-gon in P. The final section contains the equations for smoothings of simple elliptic singularitie...

Crack singularities for general elliptic systems

We consider general homogeneous Agmon-Douglis-Nirenberg elliptic systems with constant coefficients complemented by the same set of boundary conditions on both sides of a crack in a two-dimensional domain. We prove that the singular functions expressed in polar coordinates (r; ) near the crack tip all have the form r 12+k'( ) with k 0 integer, with the possible exception of a finite number of s...