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Main Title: Willmore surfaces in S^n
Author(s): Li, Haizhong
Type: Research Paper
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.
Subject(s): Willmore surface
minimal surface
Veronese surface
Issue Date: 29-Jan-2001
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 53C42 Immersions
53A10 Minimal surfaces, surfaces with prescribed mean curvature
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2001, 726
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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