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Geometry and Topology of Aspherical Manifolds

Lp-cohomology and the geometry of p-harmonic forms

Publication ,  Chapter
Stern, M
January 1, 2025

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.

Duke Scholars

DOI

Publication Date

January 1, 2025

Volume

816

Start / End Page

151 / 170

Publisher

AMS

Related Subject Headings

  • 4904 Pure mathematics
 

Citation

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Stern, M. (2025). Lp-cohomology and the geometry of p-harmonic forms. In L. F. Di Cerbo & L. G. Maxim (Eds.), Geometry and Topology of Aspherical Manifolds (Vol. 816, pp. 151–170). AMS. https://doi.org/10.1090/conm/816/16356
Stern, M. “Lp-cohomology and the geometry of p-harmonic forms.” In Geometry and Topology of Aspherical Manifolds, edited by Luca F. Di Cerbo and Laurenţiu G. Maxim, 816:151–70. AMS, 2025. https://doi.org/10.1090/conm/816/16356.
Stern M. Lp-cohomology and the geometry of p-harmonic forms. In: Di Cerbo LF, Maxim LG, editors. Geometry and Topology of Aspherical Manifolds. AMS; 2025. p. 151–70.
Stern, M. “Lp-cohomology and the geometry of p-harmonic forms.” Geometry and Topology of Aspherical Manifolds, edited by Luca F. Di Cerbo and Laurenţiu G. Maxim, vol. 816, AMS, 2025, pp. 151–70. Manual, doi:10.1090/conm/816/16356.
Stern M. Lp-cohomology and the geometry of p-harmonic forms. In: Di Cerbo LF, Maxim LG, editors. Geometry and Topology of Aspherical Manifolds. AMS; 2025. p. 151–170.

DOI

Publication Date

January 1, 2025

Volume

816

Start / End Page

151 / 170

Publisher

AMS

Related Subject Headings

  • 4904 Pure mathematics