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## Willmore surfaces in S^n

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Author(s) : Haizhong Li

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 726-2001

MSC 2000

53C42 Immersions
53A10 Minimal surfaces, surfaces with prescribed mean curvature

Abstract :
A surface $x:M\to S^n$ is called a Willmore surface if it is a critical surface of the Willmore functional. It is well-known that any minimal surface is a Willmore surface and there exist many non-minimal Willmore surfaces. In this paper, we establish an integral inequality for compact Willmore surfaces in $S^n$ and get a new characterization of the Veronese surface in $S^4$ as a Willmore surface. Our result reduces to a well-known result in the case of minimal surfaces.

Keywords : Willmore surface, minimal surface, pinching, Veronese surface