Six Problems on the Length of the Cut Locus

Vîlcu, Costin; Zamfirescu, Tudor

doi:10.1007/978-3-319-28186-5_22

Costin Vîlcu⁴ &
Tudor Zamfirescu^4,5,6

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 148))

941 Accesses

Abstract

This Note is about the length of the cut locus on convex surfaces. We formulate 6 problems. The first four deal with polyhedral surfaces, while the last two are about the cut locus with respect to an infinite set.

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

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 84.99; Price excludes VAT (USA)

Softcover Book: USD 109.99; Price excludes VAT (USA)

Hardcover Book: USD 109.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

J.J. Hebda, Metric structure of cut loci in surfaces and Ambrose’s problem. J. Diff. Geom. 40, 621–642 (1994)
MathSciNet MATH Google Scholar
J. Itoh, The length of a cut locus on a surface and Ambrose’s problem. J. Diff. Geom. 43, 642–651 (1996)
MATH Google Scholar
J. Itoh, C. Nara, C. Vîlcu, Continuous flattening of convex polyhedra. LNCS, vol. 7579, pp. 85–97 (2012)
Google Scholar
J. Itoh, T. Zamfirescu, On the length of the cut locus for finitely many points. Adv. Geom. 5, 97–106 (2005)
Article MathSciNet MATH Google Scholar
K. Shiohama, M. Tanaka, Cut loci and distance spheres on Alexandrov surfaces, in Actes de la Table Ronde de Géométrie Différentielle Sém. Congr. Soc. Math. 1996, Luminy, vol. 1 (France, Paris, 1992), pp. 531–559
Google Scholar
L. Yuan, T. Zamfirescu, On the cut locus of finite sets on convex surfaces, manuscript
Google Scholar
T. Zamfirescu, Many endpoints and few interior points of geodesics. Inventiones Math. 69, 253–257 (1982)
Article MathSciNet MATH Google Scholar
T. Zamfirescu, Extreme points of the distance function on convex surfaces. Trans. Amer. Math. Soc. 350, 1395–1406 (1998)
Article MathSciNet MATH Google Scholar

Download references

Author information

Authors and Affiliations

Institute of Mathematics “Simion Stoilow” of the Roumanian Academy, P.O. Box 1-764, 014700, Bucharest, Romania
Costin Vîlcu & Tudor Zamfirescu
Fachbereich Mathematik, Universität Dortmund, 44221, Dortmund, Germany
Tudor Zamfirescu
College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050024, People’s Republic of China
Tudor Zamfirescu

Authors

Costin Vîlcu
View author publications
You can also search for this author in PubMed Google Scholar
Tudor Zamfirescu
View author publications
You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Costin Vîlcu .

Editor information

Editors and Affiliations

Einstein Institute for Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel
Karim Adiprasito
Hungarian Academy of Sciences, Rényi Institute of Mathematics, Budapest, Hungary
Imre Bárány
Mathematics of the Roumanian Academy, ``Simion Stoilow'' Institute of, Bucharest, Romania
Costin Vilcu

Rights and permissions

Reprints and permissions

Copyright information

About this paper

Cite this paper

Vîlcu, C., Zamfirescu, T. (2016). Six Problems on the Length of the Cut Locus. In: Adiprasito, K., Bárány, I., Vilcu, C. (eds) Convexity and Discrete Geometry Including Graph Theory. Springer Proceedings in Mathematics & Statistics, vol 148. Springer, Cham. https://doi.org/10.1007/978-3-319-28186-5_22

Download citation

DOI: https://doi.org/10.1007/978-3-319-28186-5_22
Published: 03 May 2016
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-28184-1
Online ISBN: 978-3-319-28186-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

Publish with us

Policies and ethics