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Developable Surfaces with Prescribed Boundary

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Extended Abstracts GEOMVAP 2019

Part of the book series: Trends in Mathematics ((RPCRMB,volume 15))


It is proved that a generic simple, closed, piecewise regular curve in space can be the boundary of only finitely many developable surfaces with nonvanishing mean curvature. The relevance of this result in the context of the dynamics of developable surfaces is discussed.

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  1. M.P. do Carmo, Differential Geometry of Curves and Surfaces (Prentice–Hall, 1976)

    Google Scholar 

  2. F. Coltraro, Experimental validation of an inextensible cloth model, IRI Technical Report IRI-TR-20-04 (2020).

  3. M. Deserno, Fluid lipid membranes: from differential geometry to curvature stresses. Chem. Phys. Lipids 185, 11–45 (2015)

    Article  Google Scholar 

  4. Dierkes, H.,The n-dimensional analogue of the catenary. Prescribed Area, in Geometric Analysis and the Calculus of Variations, ed. by J. Jost, pp. 1–12 (International Press, 1996)

    Google Scholar 

  5. P. Fischer, Ruled Varieties. An Introduction to Algebraic Differential Geometry (Vieweg, 2001)

    Google Scholar 

  6. V.D. Sedykh, Structure of the convex hull of a space curve. J. Sov. Math. 33, 1140–1153 (1986)

    Article  Google Scholar 

  7. V. Ushakov, The explicit general solution of trivial Monge-Ampère equation. Comment. Math. Helv. 75, 125–133 (2000)

    Article  MathSciNet  Google Scholar 

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Research supported by project Clothilde, ERC research grant 741930, and research grants PID2019-103849GB-I00, from the Kingdom of Spain, 2017 SGR 932 from the Catalan Government. MAC is also with Institut de Robòtica i Informàtica Industrial (CSIC-UPC), the Institut de Matemàtiques de la UPC-BarcelonaTech (IMTech) and the Barcelona Graduate School of Mathematics (BGSMath).

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Correspondence to Maria Alberich-Carramiñana .

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Alberich-Carramiñana, M., Amorós, J., Coltraro, F. (2021). Developable Surfaces with Prescribed Boundary. In: Alberich-Carramiñana, M., Blanco, G., Gálvez Carrillo, I., Garrote-López, M., Miranda, E. (eds) Extended Abstracts GEOMVAP 2019. Trends in Mathematics(), vol 15. Birkhäuser, Cham.

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