대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제20권4호
  • /
  • Pages.775-779
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  • 2005
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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STABLE MINIMAL HYPERSURFACES IN A CRITICAL POINT EQUATION

  • 발행 : 2005.10.01
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초록

On a compact n-dimensional manifold $M^n$, a critical point of the total scalar curvature functional, restricted to the space of metrics with constant scalar curvature of volume 1, satifies the critical point equation (CPE), given by $Z_g\;=\;s_g^{1\ast}(f)$. It has been conjectured that a solution (g, f) of CPE is Einstein. The purpose of the present paper is to prove that every compact stable minimal hypersurface is in a certain hypersurface of $M^n$ under an assumption that Ker($s_g^{1\ast}{\neq}0$).

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참고문헌

  1. A. L. Besse, Einstein Manifolds, Springer-Verlag, New York, 1987
  2. A. E. Fischer and J. E. Marsden, Manifolds of Riemannian Metrics with Prescribed Scalar Curvature, Bull. Amer. Math. Soc. 80 (1974), 479-484 https://doi.org/10.1090/S0002-9904-1974-13457-9
  3. S. Hwang, Critical points and conformally fiat metrics, Bull. Korean Math. Soc. 37 (2000), no. 3, 641-648
  4. S. Hwang, Critical points of the scalar curvature funetionals on the space of meirics of constant scalar curvature, Manuscripta Math. 103 (2000), 135-142 https://doi.org/10.1007/PL00005857
  5. S. Hwang, The critical point equation on a three dimensional compact manifold, Proc. Amer. Math. Soc. 131 (2003), 3221-3230 https://doi.org/10.1090/S0002-9939-03-07165-X
  6. H. B. Lawson, Minimal varieties in real and complex geometry, University of Montreal lecture notes, 1974

피인용 문헌

  1. TOTAL SCALAR CURVATURE AND EXISTENCE OF STABLE MINIMAL SURFACES vol.30, pp.4, 2008, https://doi.org/10.5831/HMJ.2008.30.4.677