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The proper Dupin hypersurface conjecture in the four-curvature case
Proper Dupin hypersurface conjecture. Every compact embedded proper Dupin hypersurface in $S^5$ with four distinct principal curvatures is diffeomorphic to
Conjectureopendifferential-geometry isoparametric-hypersurfaces proper-dupin-hypersurfacesarXiv posted 2 days ago

The proper Dupin hypersurface conjecture in the four-curvature case