대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제29권1호
  • /
  • Pages.123-130
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  • 2014
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  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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STABLE MINIMAL HYPERSURFACES WITH WEIGHTED POINCARÉ INEQUALITY IN A RIEMANNIAN MANIFOLD

  • 투고 : 2012.09.10
  • 발행 : 2014.01.31
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초록

In this note, we investigate stable minimal hypersurfaces with weighted Poincar$\acute{e}$ inequality. We show that we still get the vanishing property without assuming that the hypersurfaces is non-totally geodesic. This generalizes a result in [2].

키워드

참고문헌

  1. X. Cheng and D. T. Zhou, Manifolds with weighted Poincare inequality and uniqueness of minimal hypersurfaces, Comm. Anal. Geom. 17 (2009), no. 1, 139-154. https://doi.org/10.4310/CAG.2009.v17.n1.a6
  2. N. T. Dung and K. Seo, Stable minimal hypersurfaces in a Riemannian manifold with pinched negative sectional curvature, Ann. Global Anal. Geom. 41 (2012), no. 4, 447-460. https://doi.org/10.1007/s10455-011-9293-x
  3. K. H. Lam, Results on a weighted Poincare inequality of complete manifolds, Trans. Amer. Math. Soc. 362 (2010), no. 10, 5043-5062. https://doi.org/10.1090/S0002-9947-10-04894-4
  4. P. F. Leung, An estimate on the Ricci curvature of a submanifold and some applications, Proc. Amer. Math. Soc. 114 (1992), no. 4, 1051-1061. https://doi.org/10.1090/S0002-9939-1992-1093601-7
  5. P. Li and J. Wang, Complete manifolds with positive spectrum, J. Differential Geom. 58 (2001), no. 3, 501-534. https://doi.org/10.4310/jdg/1090348357
  6. X. Wang, On conformally compact Einstein manifolds, Math. Res. Lett. 8 (2001), no. 5-6, 671-688. https://doi.org/10.4310/MRL.2001.v8.n5.a9

피인용 문헌

  1. L2HARMONIC 1-FORMS ON SUBMANIFOLDS WITH WEIGHTED POINCARÉ INEQUALITY vol.53, pp.3, 2016, https://doi.org/10.4134/JKMS.j150190
  2. Harmonic p-forms on Hadamard manifolds with finite total curvature pp.1572-9060, 2018, https://doi.org/10.1007/s10455-018-9609-1