Mathematical Sciences: Special Submanifolds

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9403851 Jensen This award supports mathematical research on problems in differential geometry. The work focuses on Dupin hypersurfaces and deformable surfaces in Lie Sphere geometry. Efforts will be made to determine whether or not there exist minimal surfaces with constant negative Gaussian curvature in the complex projective plane. The problems involve special submanifolds of great interest; their solutions involve a combination of techniques arising in the study of systems of partial differential equations combined with geometric structures. Applications of the work may be expected in mathematical physics as well as geometry. Differential geometry is a branch of mathematics which combines methods of analysis with geometric motivation. The problems often derive from those of the physical world such as would be found in studies of relativity, turbulence, dynamical systems and chaos. ***