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 Spec
p(
M), here
p∈{0, 1, 2, 3}. In higher dimensional sphere, we prove that if Spec
p(
M)=Spec
p(
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 Spec
p(
Mn, n) for some
p=
p(
n).
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