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On the nonexistence of stable minimal submanifolds and the Lawson–Simons conjecture

Tom 96 / 2003

Ze-Jun Hu, Guo-Xin Wei Colloquium Mathematicum 96 (2003), 213-223 MSC: 53C20, 53C40, 53C42. DOI: 10.4064/cm96-2-6

Streszczenie

Let $\, \overline {\! M}$ be a compact Riemannian manifold with sectional curvature $K_{\, \overline {\! M}}$ satisfying $1/5< K_{\, \overline {\! M}}\le 1$ (resp. $2\le K_{\, \overline {\! M}}<10$), which can be isometrically immersed as a hypersurface in the Euclidean space (resp. the unit Euclidean sphere). Then there exist no stable compact minimal submanifolds in $\, \overline {\! M}$. This extends Shen and Xu's result for ${1\over 4}$-pinched Riemannian manifolds and also suggests a modified version of the well-known Lawson–Simons conjecture.

Autorzy

  • Ze-Jun HuDepartment of Mathematics
    Zhengzhou University
    Zhengzhou 450052, P.R. China
    e-mail
  • Guo-Xin WeiDepartment of Mathematics
    Zhengzhou University
    Zhengzhou 450052, P.R. China

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