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

• Autorzy: Ze-Jun Hu , Guo-Xin Wei
• Języki publikacji: EN

Abstrakty

EN

Let M̅ be a compact Riemannian manifold with sectional curvature $K_{M̅}$ satisfying $1/5 < K_{M̅} ≤ 1$ (resp. $2 ≤ K_{M̅} < 10$), 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 M̅. This extends Shen and Xu's result for 1/4-pinched Riemannian manifolds and also suggests a modified version of the well-known Lawson-Simons conjecture.

Kategorie tematyczne

• 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
• 53C20: Global Riemannian geometry, including pinching
• 53C40: Global submanifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 96
• Numer: 2
• Strony: 213-223

Daty

wydano

2003

Twórcy

autor

Ze-Jun Hu

• Department of Mathematics, Zhengzhou University, Zhengzhou 450052, P.R. China

autor

Guo-Xin Wei

• Department of Mathematics, Zhengzhou University, Zhengzhou 450052, P.R. China

Identyfikatory

DOI

10.4064/cm96-2-6