ABSTRACT
We prove an existence theorem for a p-harmonic map from a complete manifold into a certain compact manifold, generalizing results of Eells-Sampson, Schoen-Yau and Burstall that treat the case https://www.w3.org/1998/Math/MathML">p=2https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064593/1178e5ac-b8c1-4916-83b8-0e4e91098d1a/content/eq3197.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>. We give a unified and refined estimate on the Hausdorff dimension of the singular set of p-minimizers into any p-superstrongly unstable manifold. The regularity result of a p-minimizer into an ellipsoid or the closed upper half-ellipsoid is also obtained. Liouville-type theorems for p-harmonic, p-stable and p-minimizing maps on complete manifolds into the closed upper half-ellipsoid are established.
