Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14744
 Main Title: Willmore surfaces in S^n Author(s): Li, Haizhong Type: Research Paper URI: https://depositonce.tu-berlin.de/handle/11303/15971http://dx.doi.org/10.14279/depositonce-14744 License: http://rightsstatements.org/vocab/InC/1.0/ 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 surfaceminimal surfacepinchingVeronese surface Issue Date: 29-Jan-2001 Date Available: 17-Dec-2021 Language Code: en DDC Class: 510 Mathematik MSC 2000: 53C42 Immersions53A10 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