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<i>L<sup>p</sup> p</i>-Harmonic 1-Forms on <i>δ</i>-Stable Hypersurface in Space Form with Nonnegative Bi-Ricci Curvature
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
- 1 College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
- 2 College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
Advances in Pure Mathematics·Volume 11 (2021)·Pages 427–439·Published 17 May 2021·DOI10.4236/apm.2021.115029
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Abstract
In this paper, we investigate the space of L p p -harmonic 1-forms on a complete noncompact orientable δ -stable hypersurface M m that is immersed in space form with nonnegative BiRic curvature. We prove the nonexistence of L p p -harmonic 1-forms on M m . Moreover, we obtain some vanishing properties for this class of harmonic 1-forms.
Keywords<i>L<sup>p</sup>p</i>-Harmonic 1-Forms<i>δ</i>-Stable HypersurfaceBiRic CurvatureSpace Form
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