Subelliptic harmonic maps

Subelliptic Harmonic Maps

We study a nonlinear harmonic map type system of subelliptic PDE. In particular, we solve the Dirichlet problem with image contained in a convex ball.

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...

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

The story begins with the paper of Müller, [59], who — for the sake of an application to nonlinear elasticity — proved that if the Jacobian determinant Ju of a Sobolev map u ∈ W 1,n loc (Rn ,Rn ) is nonnegative, then it belongs locally to L log L. The result is quite intriguing, since a priori Hölder inequality implies only that Ju ∈ L1 and one does not suspect any higher integrability. If one ...

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

Stable Exponentially Harmonic Maps Between Finsler Manifolds