Multi local invariants on real unit balls (Q2711345)

The author considers invariants for the real Möbius transformations acting on the real hyperbolic unit ball \(\mathbb R^n\). He also constructs multilocal invariants at several distinct points in the interior and/or at the boundary. NEWLINENEWLINENEWLINEIn the first place there is a detailed study of invariant functions and vector fields at various orders (zero, first and higher), depending only on interior points of \(B^n\). In the sequel, invariants depending on boundary and interior points are studied, again by considering various orders. NEWLINENEWLINENEWLINEThe real Möbius invariant Poisson kernel is also studied, whereas special attention is given to invariants characterizing motions of points in \(B^n\) or \(\partial B^n\). NEWLINENEWLINENEWLINESince the general methods of the paper are based on the assumption that \(n\geq 4\), the particular cases of dimensions 2 and 3 are treated separately.