On the reduced L 2 cohomology on complete hypersurfaces in Euclidean spaces

Abstract

We discuss complete noncompact hypersurfaces in the Euclidean space \({\mathbb{R}^{n+1}}\) with finite total curvature. We obtain that the reduced L2 cohomology space has finite dimension. This result is an improvement of Carron’s result without the restriction of mean curvature. It is also a generalization of the result of Cavalcante, Mirandola, and Vitorio from the case of L2 harmonic 1-forms to the case of L2 harmonic p-forms (\({0\leq p\leq n}\)).