Subelliptic Harmonic Maps

Subelliptic p-harmonic maps into spheres and the ghost of Hardy spaces

I ) Introduction 1 to CR geometry and subelliptic harmonic maps . II ) Boundary values of Bergman - harmonic maps

We give an elementary introduction to CR and pseudohermitian geometry, starting from H. Lewy’s legacy (cf. [20]) i.e. tangential Cauchy-Riemann equations on the boundary of the Siegel domain. In this context we describe fundamental objects, such as contact structures, Levi forms, the Tanaka-Webster connection and the Fefferman metric (cf. e.g. [4]). Also naturally arising Hörmander systems of v...

ON THE REGULARITY OF SUBELLIPTIC p-HARMONIC FUNCTIONS IN CARNOT GROUPS

In this paper we prove second order horizontal differentiability and C1,α regularity results for subelliptic p-harmonic functions in Carnot groups for p close to 2.

Subelliptic Cordes Estimates in the Grušin Plane

We apply subelliptic Cordes conditions and Talenti-Pucci type inequalities to prove W 2,2 and C estimates for p-harmonic functions in the Grušin plane for p near 2.

Invariant Wave Maps from Gödel’s Universe

Gödel’s metric is a solution g↵ to the Einstein field equations, with cosmological constant, in the presence of an incoherent matter distribution. Gödel’s universe G4 ↵ = R4 , g↵ is the total space of a principal bundle R ! G4 ↵ ! M3 over a 3dimensional nondegenerate CR manifold M3 = G4 ↵/K got as the space of orbits of a null Killing vector field K on G4 ↵. Invariant wave maps : G4 ↵ ! N are p...