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Variations of Surfaces

  • 章节

  • 出版模式：

    开放获取

  • 发表日期：

    2024年

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  • Ulrich Pinkall,
  • Oliver Gross

摘要

We derive the basics of Vector Calculus on surfaces and explore variations of surfaces. In particular, we compute the variational derivative of the area form \(\det \) and of the shape operator A. We show that the critical points of the area functional are the surfaces with mean curvature \(H=0\) .