L^(p)Harmonic k-forms on Complete Noncompact Hypersurfaces in S^(n+1) with Finite Total Curvature  

作　　者：Jiuru Zhou 

机构地区：[1]School of Mathematical Sciences,Yangzhou University,Yangzhou 225002,China

出　　处：《Journal of Mathematical Study》2021年第4期396-406,共11页数学研究（英文）

基　　金：supported by National Natural Science Foundation of China(Grant No.11771377);the Natural Science Foundation of Jiangsu Province(Grant No.BK20191435).

摘　　要：In general,the space of Lp harmonic forms H^(k)(Lp(M))and reduced Lp cohomology Hk(L^(p)(M))might be not isomorphic on a complete Riemannian manifold M,except for p=2.Nevertheless,one can consider whether dimH^(k)(Lp(M))<+∞are equivalent to dimHk(Lp(M))<+¥.In order to study such kind of problems,this paper obtains that dimension of space of Lp harmonic forms on a hypersurface in unit spherewith 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 Lp cohomology on such hypersurfaces.

关 键 词：L^(p)harmonic k-form hypersurface in sphere total curvature 

分 类 号：O18[理学—数学]