@Article{JMS-54-4,
author = {Zhou, Jiuru},
title = {$L^p$ Harmonic $k$-Forms on Complete Noncompact Hypersurfaces in $\mathbb{S}^{n+1}$ with Finite Total Curvature},
journal = {Journal of Mathematical Study},
year = {2021},
volume = {54},
number = {4},
pages = {396--406},
abstract = {<p style="text-align: justify;">In general, the space of $L^p$ harmonic forms $\mathcal{H}^k(L^p(M))$ and reduced $L^p$ cohomology $H^k(L^p(M))$ might be not isomorphic on a complete Riemannian manifold $M$, except for $p=2$. Nevertheless, one can consider whether $\mathrm{dim}\mathcal{H}^k(L^p(M))&lt;+\infty$ are equivalent to $\mathrm{dim}H^k(L^p(M))&lt;+\infty$. In order to study such kind of problems, this paper obtains that dimension of space of $L^p$ harmonic forms on a hypersurface in unit sphere with finite total curvature is finite, which is also a generalization of the previous work by Zhu. The next step will be the investigation of dimension of the reduced $L^p$ cohomology on such hypersurfaces.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v54n4.21.05},
url = {https://global-sci.com/article/87683/lp-harmonic-k-forms-on-complete-noncompact-hypersurfaces-in-mathbbsn1-with-finite-total-curvature}
}