# On total curvature of immersions and minimal submanifolds of spheres

Commentationes Mathematicae Universitatis Carolinae (1993)

- Volume: 34, Issue: 3, page 459-463
- ISSN: 0010-2628

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topRotondaro, Giovanni. "On total curvature of immersions and minimal submanifolds of spheres." Commentationes Mathematicae Universitatis Carolinae 34.3 (1993): 459-463. <http://eudml.org/doc/247484>.

@article{Rotondaro1993,

abstract = {For closed immersed submanifolds of Euclidean spaces, we prove that $\int |\mu |^2\, dV\ge V/R^2$, 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.},

author = {Rotondaro, Giovanni},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {closed submanifold; total mean curvature; minimal submanifold; Willmore conjecture; total mean curvature},

language = {eng},

number = {3},

pages = {459-463},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {On total curvature of immersions and minimal submanifolds of spheres},

url = {http://eudml.org/doc/247484},

volume = {34},

year = {1993},

}

TY - JOUR

AU - Rotondaro, Giovanni

TI - On total curvature of immersions and minimal submanifolds of spheres

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1993

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 34

IS - 3

SP - 459

EP - 463

AB - For closed immersed submanifolds of Euclidean spaces, we prove that $\int |\mu |^2\, dV\ge V/R^2$, 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.

LA - eng

KW - closed submanifold; total mean curvature; minimal submanifold; Willmore conjecture; total mean curvature

UR - http://eudml.org/doc/247484

ER -

## References

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