Mathematical Sciences: Analysis on Manifolds

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Peter Li and Andrejs Treibergs both have very strong research reputations arising from their work in partial differential equations. The techniques they have been using have proved very powerful in the study of manifolds. In the current project Professor Li will continue his investigations into the effect of curvature on the space of harmonic functions on a manifold. More specifically he will study the underlying geometry via estimates of the first eigenvalue of the Laplacian. Professor Treibergs will work on problems concerned with the realization of surfaces with prescribed curvature. In particular he will try to establish existence results under integral conditions weaker than those previously employed.