n-harmonic maps and geometries of conformal structures on Riemannian manifolds

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In this research, we studied n-harmonic maps and p-harmonic maps. Kawai and Nakauchi gave estimates of Dirichlet p-eigenvalue problems on p-Laplacian using the exponent p and the diameter of source manifolds. In this proof, we utilized, as key lemmas, formulas of Bochner-Weitzenbock type for a certain linear operater, which depends on the exponent p, inplace of the ordinary Bochner technique for the Laplacian. Kawai proved that there exists no L^2-elgen spinor for nonzero eigenvalue on noncompact complete Riemannian manifolds with poles. Takakuwa proved compactness of spaces of harmonic maps and Yang-Mills connections under some conditions.