Lp -cohomology and the geometry of p-harmonic forms

Abstract

In this note we describe basic geometric properties of p-harmonic forms and p-coclosed forms and use them to reprove vanishing theorems of Pansu and new injectivity theorems for the Lp -cohomology of simply connected, pinched negatively curved manifolds. We also provide a partial resolution of a conjecture of Gromov on the vanishing of Lp -cohomology on symmetric spaces.

arXiv comment17 pages. Comments welcome. Results depending on the Hodge decomposition of reference [Ama17] removed