$L_f^p$ harmonic 1-forms on complete non-compact smooth metric measure spaces

Jiuru Zhou, Peng Zhu

This paper studies complete non-compact smooth metric measure space $(M^n,g,{\mathrm{e}}^{-f}\mathrm{d}v)$ with positive first spectrum ${\lambda }_1({\Delta }_f)$ or satisfying a weighted Poincaré i…