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