Many common finite p-groups admit automorphisms of order coprime to p, and when p is odd, it is reasonably difficult to find finite p-groups with automorphism group a p-group. Yet the goal of this paper is to prove that almost all finite p-groups do have automorphism group a p-group when p is odd. The asymptotic sense in which the theorem holds involves bounding the Frattini length of the p-gro...

In previous work with A. Vasy and J. Wunsch, the author established an asymptotic expansion for the radiation field on asymptotically Minkowski spacetimes and showed that the exponents seen in the expansion are given by the poles of a meromorphic family of operators on the spacetime’s “boundary at infinity”. This note provides an explicit accounting of these poles when the spacetime is 3 + 1-di...

A family of asymptotic solutions at infinity for the system of ordinary differential equations is considered. Existence of exact solutions which have these asymptotics is proved.

We find new classes of exact string solutions in a variety of curved backgrounds. They include stationary and dynamical (open, closed, straight, finitely and infinitely long) strings as well as multi-string solutions, in terms of elliptic functions. The physical properties, string length, energy and pressure are computed and analyzed. In anti de Sitter spacetime, the solutions describe an infin...

We prove a general maximum principle at infinity for properly immersed minimal surfaces with boundary in R. An important corollary of this maximum principle at infinity is the existence of a fixed sized regular neighborhood for any properly embedded minimal surface of bounded curvature.

This survey paper discusses five equivalent ways of defining a “critical point at infinity” for a complex polynomial of two variables.

This paper studies certain inverse problems in the optimal frequency-domain synthesis of robust controllers, in both the 2-norm and the infinity-norm. These inverse problems identify the class of controllers which are optimal for some choice of weights. Their implications for loopshaping are discussed.

We investigate a version of the Phragmén–Lindelöf theorem for solutions of the equation ∆∞u = 0 in unbounded convex domains. The method of proof is to consider this infinity harmonic equation as the limit of the p-harmonic equation when p tends to ∞.