Skip to main content

Developable Surfaces with Prescribed Boundary

  • Conference paper
  • First Online:
Extended Abstracts GEOMVAP 2019

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

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  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). http://hdl.handle.net/2117/331210

  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 

Download references

Acknowledgements

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).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Maria Alberich-Carramiñana .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

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. https://doi.org/10.1007/978-3-030-84800-2_21

Download citation

Publish with us

Policies and ethics