On spectral characterizations of minimal hypersurfaces in a sphere

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Let M be a closed minimal hypersurface in an Euclidean sphere Sn+1(1). We first prove that a minimal isoparametric hypersurface M in a 4-dimensional sphere is completely determined by its spectrum Specp(M), here p∈{0, 1, 2, 3}. In higher dimensional sphere, we prove that if Specp(M)=Specp(Mm, n−m) for p=0, 1, where Mm, n−m=Sm(√{\frac{m}{n}})×Sn−m(√{\frac{n−m}{n}}) is a Clifford torus, then M is Mm, n−m. Furthermore, we prove that Mn, n→S2n+1(1) (n{≥}4) is also characterized by Specp(Mn, n) for some p=p(n).
国立大学法人東京工業大学大学院理工学研究科数学専攻の論文