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On stable compact minimal submanifolds
stability minimal submanifolds product spaces spheres
2011/1/18
Stable compact minimal submanifolds of the product of a sphere and any Riemannian manifold are classified whenever the dimension of the sphere is at least three. The complete classification of the sta...
Embeddedness of proper minimal submanifolds in homogeneous spaces
minimal submanifolds homogeneous spaces
2010/11/23
We prove the three embeddedness results as follows. $({\rm i})$ Let $\Gamma_{2m+1}$ be a piecewise geodesic Jordan curve with $2m+1$ vertices in $\mathbb{R}^n$, where $m$ is an integer $\geq2$. Then t...