Mathematical Sciences: Geometry of Submanifolds/InjectivityProblems in Geometry

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Professor Smyth will continue his research on sets of principal curvatures of hypersurfaces in Euclidean space and to extend some of the techniques previously developed to spaces of constant curvature. The anticipated results may be employed to obtain some interesting generalizations of previous classical results for isoparametric hypersurfaces. Xavier will continue his research on the study of complete embedded simply-connected minimal surfaces and relationships with algebraic curve geometry.