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Polynomial Approximation in Sobolev Spaces on the Unit Sphere and the Unit Ball
Polynomial Sobolev Spaces Unit Sphere Unit Ball
2010/11/18
This work is a continuation of the recent study by the authors on approximation theory over the sphere and the ball. The main results define new Sobolev spaces on these domains and study polynomial ap...
Rigidity Theorem of Hypersurfaces with Constant Scalar Curvature in a Unit Sphere
principal curvature Clifford torus Gauss equations
2007/12/12
In this paper, we give a characterization of tori $S^1\left(\sqrt{\frac{nr+2-n}{nr}}\right)\times S^{n-1}\left(\sqrt{\frac{n-2}{nr}}\right)$ and $S^m\left(\sqrt{\frac{m}{n}}\right)\times S^{n-m}\left(...
The Isometric Extension of the into Mapping from the Unit Sphere $S(l^\infty_{(2)})$ to $S(L^1(\mu))^1$
isometric mapping isometric extension
2007/12/12
This is the first paper to consider the isometric extension problem of an into-mapping between the unit spheres of two different types of spaces. We prove that, under some conditions, an into-isometri...