On reduced L² cohomology of hypersurfaces in spheres with finite total curvature

Abstract

In this paper, we prove that the dimension of the second space of reduced L² cohomology of M is finite if is a complete noncompact hypersurface in a sphere 𝕊ⁿ⁺¹and has finite total curvature (n≥3).

total curvature; reduced L² cohomology; hypersurface in sphere; L² harmonic 2-form