We prove that there exist no stable minimal submanifolds in some n-dimensional ellipsoids, which generalizes J. Simons' result about the unit sphere and gives a partial answer to Lawson–Simons' conjecture.
@article{bwmeta1.element.bwnjournal-article-cmv73i1p1bwm,
author = {Haizhong Li},
title = {Some nonexistence theorems on stable minimal submanifolds},
journal = {Colloquium Mathematicae},
volume = {72},
year = {1997},
pages = {1-13},
zbl = {0880.53050},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv73i1p1bwm}
}
Li, Haizhong. Some nonexistence theorems on stable minimal submanifolds. Colloquium Mathematicae, Tome 72 (1997) pp. 1-13. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv73i1p1bwm/
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