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A global pinching theorem for surfaces with constant mean curvature in

Authors:	Yi-Jung Hsu Tai-Ho Wang

Institution:	Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan ; Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan

Abstract:	Let be a compact immersed surface in the unit sphere with constant mean curvature . Denote by $\phi$ the linear map from into , $\phi=A-\frac H2I$ , where is the linear map associated to the second fundamental form and is the identity map. Let $\Phi$ denote the square of the length of $\phi$ . We prove that if $\vert\vert\Phi\vert\vert _{L^2}\leq C$ , then is either totally umbilical or an -torus, where is a constant depending only on the mean curvature .

Keywords:	Mean curvature sphere totally umbilical

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