Mathematical Sciences: Research in Differential Geometry andTopology

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8900285 Meeks The principal investigator will study a variety of problems in differential geometry and differential topology. The main goal of the research is to develop a deeper understanding of global topological and geometrical properties of surfaces in 3-space that satisfy some nice geometrical or variational principle. Particular emphasis will be placed upon: 1. The global geometry and topology of properly embedded minimal surfaces: existence theorems, topological obstructions, total curvature theorems, conformal structure, topological uniqueness, computation of the index of examples, extension of isometries, uniqueness of minimal graphs of sublinear growth over domains with noncompact boundary. 2. Global geometry of constant mean curvature surfaces in 3-space and hyperbolic 3-space.3. Computation relevant to problems in the subject. 4. Geometry of isotopy surfaces in 3-space.