论文标题
$ l_f^p $谐波1形，完全非压缩平滑度量度量空间
$L_f^p$ harmonic 1-forms on complete non-compact smooth metric measure spaces
论文作者
论文摘要
本文研究完成了非紧凑的平滑度量测量空间$（m^n，g，\ m artrm {e}^{ - f} \ mathrm {d} v）$，带有正谱$λ_1（Δ_F）$或满足加权Poincaré与权重函数$ρ$ρ$ρ$。我们在假设$ $ m $ -bakry-émeryricci曲率$ \ mathrm {ric} _ {m，n} \ geq-geq-aλ_1（Δ_f）$ n geq-geq n geq ricmatrm {mathrm {mathrm {ric} __________________________________________________________________________________ m特定常数$ a $和$ b> 0 $的-aρ -b $。这些结果灵感来自汉·林的工作，是粪便和vieira先前作品的$ l_f^p $概括，$ l^2 $谐波$ 1 $ - forms。
This paper studies complete non-compact smooth metric measure space $(M^n,g,\mathrm{e}^{-f}\mathrm{d}v)$ with positive first spectrum $λ_1(Δ_f)$ or satisfying a weighted Poincaré inequality with weight function $ρ$. We establish two splitting and vanishing theorems for $L_f^p$ harmonic $1$-forms under the assumption that $m$-Bakry-Émery Ricci curvature $\mathrm{Ric}_{m,n}\geq -aλ_1(Δ_f)$ or $\mathrm{Ric}_{m,n}\geq -aρ-b$ for particular constants $a$ and $b>0$. These results are inspired by the work of Han-Lin and are $L_f^p$ generalizations of previous works by Dung-Sung and Vieira for $L^2$ harmonic $1$-forms.
