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Quantization of Curvature for Compact Surfaces in S^n

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Author(s) : Haizhong Li, Udo Simon

Preprint series of the Institute of Mathematics, Technische Universität Berlin

MSC 2000

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

Abstract :
For minimal surfaces in spheres, there is a well known conjecture about the quantization of intrinsic curvature which has been solved only in special cases so far. We recall an intrinsic and an extrinsic version for the known results and extend them to compact non-minimal surfaces in spheres. In particular we discuss special classes like Willmore surfaces and surfaces with parallel mean curvature vector.

Keywords : Minimal surfaces in spheres, quantization of curvature, mean curvature vector, Veronese surface, Willmore surface

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