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

Ze-Jun Hu, and Guo-Xin Wei. "On the nonexistence of stable minimal submanifolds and the Lawson-Simons conjecture." Colloquium Mathematicae 96.2 (2003): 213-223. <http://eudml.org/doc/284869>.

@article{Ze2003,
abstract = {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.},
author = {Ze-Jun Hu, Guo-Xin Wei},
journal = {Colloquium Mathematicae},
keywords = {-pinched Riemannian manifold; compact stable minimal submanifold; compact connected hypersurface; instability; critical point of the volume functional; second variation of the volume; normal deformation; sectional curvature; Lawson-Simons conjecture},
language = {eng},
number = {2},
pages = {213-223},
title = {On the nonexistence of stable minimal submanifolds and the Lawson-Simons conjecture},
url = {http://eudml.org/doc/284869},
volume = {96},
year = {2003},
}

TY - JOUR
AU - Ze-Jun Hu
AU - Guo-Xin Wei
TI - On the nonexistence of stable minimal submanifolds and the Lawson-Simons conjecture
JO - Colloquium Mathematicae
PY - 2003
VL - 96
IS - 2
SP - 213
EP - 223
AB - 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.
LA - eng
KW - -pinched Riemannian manifold; compact stable minimal submanifold; compact connected hypersurface; instability; critical point of the volume functional; second variation of the volume; normal deformation; sectional curvature; Lawson-Simons conjecture
UR - http://eudml.org/doc/284869
ER -