On stable currents in positively pinched curved hypersurfaces

• Autorzy: Jintang Li
• Języki publikacji: EN

Abstrakty

EN

Let Mⁿ (n ≥ 3) be an n-dimensional complete hypersurface in a real space form N(c) (c ≥ 0). We prove that if the sectional curvature $K_{M}$ of M satisfies the following pinching condition: $c + δ < K_{M} ≤ c + 1$, where δ = 1/5 for n ≥ 4 and δ = 1/4 for n = 3, then there are no stable currents (or stable varifolds) in M. This is a positive answer to the well-known conjecture of Lawson and Simons.

Kategorie tematyczne

• 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
• 58A25: Currents

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 98
• Numer: 1
• Strony: 79-86

Daty

wydano

2003

Twórcy

autor

Jintang Li

• Department of Mathematics, Xiammen University, 361005 Xiammen, Fujian, P.R. China

Identyfikatory

DOI

10.4064/cm98-1-6