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On the Bryant conjecture for minimal hypersurfaces in $S^4$
We prove that a local minimal hypersurface $M^3$ in the unit sphere $S^4$ with constant scalar curvature and three distinct principal curvatures at every point must be locally congruent to the minimal Cartan isoparametric hypersurface in $S^4$, which provides a positive answer to the Bryant conjectu
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