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 of M satisfies the following pinching condition: , 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm98-1-6,
author = {Jintang Li},
title = {On stable currents in positively pinched curved hypersurfaces},
journal = {Colloquium Mathematicae},
volume = {96},
year = {2003},
pages = {79-86},
zbl = {1053.53039},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm98-1-6}
}
Jintang Li. On stable currents in positively pinched curved hypersurfaces. Colloquium Mathematicae, Tome 96 (2003) pp. 79-86. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm98-1-6/