Titlebook: Differential Geometry; From Elastic Curves Ulrich Pinkall,Oliver Gross Textbook‘‘‘‘‘‘‘‘ 2024 The Editor(s) (if applicable) and The Author(

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Manuel Posada de la Paz,Stephen C. GroftFor a curve ., global quantities like the length or the bending energy were defined as integrals over arclength of certain functions on ..

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Bobbie Ann Austin,Ami D. GadhiaFrom this chapter on we will focus attention on surfaces .. The most fundamental tool for analysing such a surface is its unit normal field . which is a map to the unit sphere ..

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New Therapeutic Uses for Existing DrugsIf we know a plane curve . near its end points, we know its total curvature . up to an integer multiple of ..

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Bobbie Ann Austin,Ami D. GadhiaWe define a . as a surface . whose boundary components have been matched in pairs in such a way that . as well as its unit normal . are continuous across the boundary. This allows us to prove an analog of the fact that the tangent winding number of a closed plane curve is an integer.

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Sylvie Grégoire,Norman Barton,David WhitemanThe analog for a surface . of the bending energy . is the ..

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Variations of CurvesMany important special curves . arise by minimizing a certain variational energy ..