arXiv subjects
Publications and source records attributed to Gautier Dietrich.
In this short note, we compute the conformal stereographic projection on the standard metric of a sphere quotient. The result is a Majumdar-Papapetrou metric, which might be useful.
We propose a global invariant $σ_c$ for contact manifolds which admit a strictly pseudoconvex CR structure, analogous to the Yamabe invariant $σ$. We prove that this invariant is non-decreasing under handle attaching and under connected sum. We then give a lower bound on $σ_c$ in a particular case.
We develop the notion of renormalized energy in CR geometry, for maps from a strictly pseudoconvex pseudohermitian manifold to a Riemannian manifold. This energy is a CR invariant functional, whose critical points, which we call CR-harmonic maps, satisfy a CR covariant subelliptic partial differential equation. The corresponding operator coincides on functions with the CR Paneitz operator.