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arXiv · 2403.19481

Lp -cohomology and the geometry of p-harmonic forms

Mark A. Stern
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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.

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Mark A. Stern. 2024-03-28. Lp -cohomology and the geometry of p-harmonic forms. https://arxiv.org/abs/2403.19481

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