Willmore surfaces in S-n

作者：Li HZ

来源：Annals of Global Analysis and Geometry, 2002, 21(2): 203-213.

DOI：10.1023/A:1014759309675

• Willmore surface
• minimal surface
• pinching
• Veronese surface

A surface x: M --> S-n is called a Willmore surface if it is a critic al surface of the Willmore functional. It is well known that any minimal surface is a Willmore surface and that many nonminimal Willmore surfaces exists. In this paper, we establish an integral inequality for compact Willmore surfaces in S-n and obtain 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.

• 出版日期2002-4
• 单位清华大学