English

Lp -cohomology and the geometry of p-harmonic forms

Differential Geometry 2024-09-04 v2

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.

Keywords

Cite

@article{arxiv.2403.19481,
  title  = {Lp -cohomology and the geometry of p-harmonic forms},
  author = {Mark A. Stern},
  journal= {arXiv preprint arXiv:2403.19481},
  year   = {2024}
}

Comments

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