On stable currents in positively pinched curved hypersurfaces

Jintang Li. "On stable currents in positively pinched curved hypersurfaces." Colloquium Mathematicae 98.1 (2003): 79-86. <http://eudml.org/doc/285073>.

@article{JintangLi2003,
abstract = {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.},
author = {Jintang Li},
journal = {Colloquium Mathematicae},
keywords = {stable currents},
language = {eng},
number = {1},
pages = {79-86},
title = {On stable currents in positively pinched curved hypersurfaces},
url = {http://eudml.org/doc/285073},
volume = {98},
year = {2003},
}

TY - JOUR
AU - Jintang Li
TI - On stable currents in positively pinched curved hypersurfaces
JO - Colloquium Mathematicae
PY - 2003
VL - 98
IS - 1
SP - 79
EP - 86
AB - 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.
LA - eng
KW - stable currents
UR - http://eudml.org/doc/285073
ER -