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Using the generalized Yau parameter method and the Sylvester theory, we verify that if M is a compact minimal hypersurface in Sn+1 whose squared length of the second fundamental form satisfies 0≤|A|2−n≤n22, then |A|2≡n and M is a Clifford torus. Moreover, we prove that if M is a complete self-shrinker with polynomial volume growth in Rn+1, and if the squared length of the second fundamental form of...
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