Abstract
In this paper, we study a complete submanifold $$M^m$$ in a sphere $$S^{m+l}$$ . We obtain that there is no nontrivial $$L^{2\beta }$$ p-harmonic 1-forms on $$M^m$$ if the total curvature is bounded from above by a constant depending only on m, and we also obtain that $$M^m$$ has only one p-nonparabolic end.
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