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The classification of minimal hypersurfaces in the unit n-dimensional sphere is a well-known subclass of problems of the classification of minimal submanifolds in Riemannian manifolds, which obey certain extrinsic restrictions for Ricci curvature or scalar curvature. In this talk, we will focus on the Laplacian and the behaviour of its first eigenvalue for minimal hypersurfaces in the unit sphere S^n, which is directly related to the Yau’s conjecture on the first eigenvalue. By incorporating the Ricci flow, we will find out what the flow of eigenvalues looks like under the assumption that the minimality and the Ricci curvature constraint are preserved, given the fixed initial conditions. Combining the monotonicity relation for eigenvalues, instability and the geometry of minimal hypersurfaces in S^n, we obtain an estimate for the first eigenvalue.