Displaying similar documents to “A bridge principle for minimal and constant mean curvature submanifolds of RN.”

On total curvature of immersions and minimal submanifolds of spheres

Giovanni Rotondaro (1993)

Commentationes Mathematicae Universitatis Carolinae

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For closed immersed submanifolds of Euclidean spaces, we prove that | μ | 2 d V V / R 2 , where μ 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.