On total curvature of immersions and minimal submanifolds of spheres
Rotondaro, Giovanni
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993), p. 459-463 / Harvested from Czech Digital Mathematics Library
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For closed immersed submanifolds of Euclidean spaces, we prove that $\int |\mu |^2\, dV\geq V/R^2$, where $\mu $ is the mean curvature field, $V$ the volume of the given submanifold and $R$ is the radius of the smallest sphere enclosing the submanifold. Moreover, we prove that the equality holds only for minimal submanifolds of this sphere.

Publié le : 1993-01-01
Classification:  53A05,  53C40,  53C42,  53C45,  58E12 
@article{118603,
     author = {Giovanni Rotondaro},
     title = {On total curvature of immersions and minimal submanifolds of spheres},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {34},
     year = {1993},
     pages = {459-463},
     zbl = {0787.53049},
     mrnumber = {1243078},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118603}
}

Rotondaro, Giovanni. On total curvature of immersions and minimal submanifolds of spheres. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 459-463. http://gdmltest.u-ga.fr/item/118603/

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