Relative L^p-cohomology and application to Heintze groups - Sequeira, Emiliano (Annales Fennici Mathematici, 2024)
We introduce the notion of relative \(L^p\)-cohomology as a quasi-isometry invariant defined for a Gromov-hyperbolic space and a point on its boundary at infinity and reproduce some basic properties of \(L^p\)-cohomology in this context. In the case of degree 1 we show a relation between the relative and the classical \(L^p\)-cohomology. As an application, we explicitly construct non-zero relative \(L^p\)-cohomology classes for a purely real Heintze group of the form \(R^n-1 times_αR\), which gives a way to prove that the eigenvalues of \(α\), up to a scalar multiple, are invariant under quasi-isometries.