Mathematical Sciences: Research in Global Differential Geometry

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Michael Anderson will carry out research in the following areas of global differential geometry: (1)The Laplace-Beltrami operator on complete Riemannian manifolds; (2)Minimal varieties, including relations with curvature integrals and Riemannian geometry; (3)Structure of manifolds of non-positive curvature and without conjugate points; (4)Structure of manifolds of non- negative Ricci and scalar curvature. In particular he will investigate the uniqueness of the tangent cone at infinity of a complete minimal surface of bounded total Gauss-Kronecker curvature. He will also continue his investigations of Hopf's conjecture that a Riemannian metric on on the torus without conjugate points is flat. The basic objective of the research concerning manifolds of non-positive curvature is to find relations between the fundamental group and the geometric properties of the manifold.