This project will support investigation of three problems concerning elliptic partial differential equations. The first problem is to obtain sharp estimates and exact expressions for eigenvalues and bifurcation points. The second problem is to establish existence theorems for smooth hypersurfaces with prescribed mean curvature in general Riemann spaces, and the third problem is to establish existence theorems for hypersurfaces with prescribed elementary symmetric function of the principal normal curvatures. These problems come from questions in Continuum Mechanics and Differential Geometry. Results from this project have potential applications in areas such as the development of new materials and the computation of stresses in static structures.
