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Korean Mathematical Society (대한수학회)
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SOME REMARKS ON STABLE MINIMAL SURFACES IN THE CRITICAL POINT OF THE TOTAL SCALAR CURVATURE

  • Published : 2008.10.31
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Abstract

It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics. When the domain of S is restricted to the space of constant scalar curvature metrics, there has been a conjecture that a critical point is isometric to a standard sphere. In this paper we investigate the relationship between the first Betti number and stable minimal surfaces, and study the analytic properties of stable minimal surfaces in M for n = 3.

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References

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Cited by

  1. THREE DIMENSIONAL CRITICAL POINT OF THE TOTAL SCALAR CURVATURE vol.50, pp.3, 2013, https://doi.org/10.4134/BKMS.2013.50.3.867
  2. Rigidity of the critical point equation vol.283, pp.6, 2010, https://doi.org/10.1002/mana.200710037