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STABLE MINIMAL HYPERSURFACES WITH WEIGHTED POINCARÉ INEQUALITY IN A RIEMANNIAN MANIFOLD

Nguyen, Dinh Sang;Nguyen, Thi Thanh

  • Received : 2012.09.10
  • Published : 2014.01.31

Abstract

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].

Keywords

minimal hypersurface;stability;weighted Poincar$\acute{e}$ inequality

References

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Cited by

  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