Mathematical Sciences: Research Project in Minimal Surfaces and Harmonic Maps
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{'SignBlockName': 'Trudy T. Sensibaugh', 'PO_EMAI': None, 'PO_PHON': None}
Mario Micallef will continue his work in the following three               areas: Riemannian manifolds with non-negative curvature on                      isotropic two-planes; minimal surfaces in flat tori; harmonic                   maps between complete, negatively curved manifolds.                                  The notion of curvature on isotropic two-planes was                        introduced recently in joint work of Micallef and Moore.                        Positivity of this curvature seems to be the correct                            generalization of such classical notions as pinching of the                     sectional curvature and positive curvature operator. Micallef                   will proceed furhter towards a classification of compact                        manifolds which admit metrics of positive curvature on isotropic                two-planes.                                                                          The study of minimal surfaces in flat tori will hopefully                  yield the first examples of stable minimal surfaces in manifolds                of non-negative sectional curvature which are not holomorphic                   with respect to any Kahler structure on the ambient manifold.
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{'Code': '1265', 'Text': 'GEOMETRIC ANALYSIS'}
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