n-harmonic maps with applications to geometry of conformal structures on manifolds

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We studied n-harmonic maps and more generally p-harmonic maps for applications to the geometry of conformal structures. Nakauchi and Kawai gave some estimates for the first eigenvalue of the p-Lapalacian. We obtained an estimate of Lichnerowicz type if the Ricci curvature is bounded from below by a positive constant, and an estimate of Li-Yau type if the Ricci curvature is non-negative. In our proof of these estimates, we used Bochner-Weitzonbeck formulas of different types. The estimate of Lichnerowicz type was proved for more general class. Kawai investigated Kato type inequalities for p-harmonic maps, and got some estimates. Takakuwa studied behaviors of solution of certain nonlinear elliptic systems, and gave an estimate on the first order derivatives. He also proved uniqueness of solutions of such elliptic systems on bounded domains in the Euclidean space, using a kind of Pohozaev identity. With such supports from various spects, Nakauchi studied n-harmonic maps, and gave a relationship between n-harmonic maps and conformal Killing vector fields.