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STABLE MINIMAL HYPERSURFACES WITH WEIGHTED POINCARE INEQUALITY IN A RIEMANNIAN MANIFOLD

Nguyen Dinh Sang|Nguyen Thi Thanh
대한수학회 (The Korean Mathematical Society)|2014.01|대한수학회논문집 (Communications of the KMS)|제29권 제1호|pp. 123-130

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참고문헌

키워드

stabilityminimal hypersurfaceweighted Poincare inequality
주제분류수학

초록

In this note, we investigate stable minimal hypersurfaces with weighted Poincar´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].

Abstract

In this note, we investigate stable minimal hypersurfaces with weighted Poincar´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].

참고문헌 (6)

  1. X. Cheng, "Manifolds with weighted Poincare inequality and uniqueness of minimal hypersurfaces", Comm. Anal. Geom, 17(1), pp.139~154 (2009)
  2. N. T. Dung, "Stable minimal hypersurfaces in a Riemannian manifold with pinched negative sectional curvature", Ann. Global Anal. Geom, 41(4), pp.447~460 (2012)
  3. K. H. Lam, "Results on a weighted Poincare inequality of complete manifolds", Trans. Amer. Math. Soc, 362(10), pp.5043~5062 (2010)
  4. P. F. Leung, "An estimate on the Ricci curvature of a submanifold and some applications", Proc. Amer. Math. Soc, 114(4), pp.1051~1061 (1992)
  5. P. Li, "Complete manifolds with positive spectrum", J. Differential Geom, 58(3), pp.501~534 (2001)
  6. X. Wang, "On conformally compact Einstein manifolds", Math. Res. Lett, 8(5-6), pp.671~688 (2001)

관련 논문AI추천

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