Harmonic Maps and a Pinching Theorem for Positively Curved Hypersurfaces
Harmonic Maps and a Pinching Theorem for Positively Curved Hypersurfaces
In this paper, we establish a theorem of Liouville type for stable harmonic maps in sufficiently pinched, positively curved hypersurfaces of a space form with nonnegative constant curvature. Similar results for the Euclidean sphere ${S^n}$ have been proved by Y. L. Xin and P. F. Leung, respectively.