Costin Vîlcu - Publications

    BOOK: Convexity and Discrete Geometry Including Graph Theory (with K. Adiprasito and I. Bárány, Eds.), Springer Proceedings in Mathematics & Statistics vol. 148 (2016).

  • Double normals of most convex bodies (with A. Riviere, J. Rouyer, and T. Zamfirescu), Adv. Math. 343 (2019) 245-272; preliminary arXiv version.
  • Farthest points on flat surfaces (with J. Rouyer), J. Geom. 109 (3) (2018), (10 pages); preliminary arXiv version.
  • Polyhedra with simple dense geodesics (with J. Itoh and J. Rouyer), arXiv version.
  • Farthest points on most Alexandrov surfaces (with J. Rouyer), Adv. Geom., to appear; [15 pages]; arXiv version.
  • On the geometry of Alexandrov surfaces, in G. Ambrus et al. (Eds.), Discrete Geometry and Convexity in Honour of Imre Bárány, Alfréd Réyi Institute of Mathematics Publishing House, 2017, 150-151; ISBN: 978 963 279 963 6.
  • Envelopes of α-sections (with N. Chevallier and A. Fruchard), in K. Adiprasito et al. (Eds.), Convexity and Discrete Geometry Including Graph Theory, Springer Proc. in Math. & Stat. vol. 148 (2016), 193-218; preliminary arXiv version.
  • Six Problems on the Length of the Cut Locus (with T. Zamfirescu), in K. Adiprasito et al. (Eds.), Convexity and Discrete Geometry Including Graph Theory, Springer Proc. in Math. & Stat. vol. 148 (2016), 257-259.
  • Simple closed geodesics on most Alexandrov surfaces (with J. Rouyer), Adv. Math. 278 (2015), 103-120; preliminary arXiv version.
  • Moderate smoothness of most Alexandrov surfaces (with J. Itoh and J. Rouyer), Int. J. Math. 26 (2015), [14 pages], DOI: 10.1142/S0129167X15400042; preliminary arXiv version.
  • Every graph is a cut locus (with J. Itoh), J. Math. Soc. Japan 67 (2015), 1227-1238; preliminary arXiv version.
  • On the Theorem of the Three Perpendiculars (with J. Itoh and J. Rouyer), Elem. Math. 70 (2015), 71-78; preliminary arXiv version.
  • Development of curves on polyhedra via conical existence (with J. O'Rourke), Comput. Geom. Theory Appl. 47 (2014), 149-163; preliminary arXiv version; also in Proc. 23rd Canadian Conference on Computational Geometry (CCCG'11), 71-76.
  • The connected components of the space of Alexandrov surfaces (with J. Rouyer), in D. Ibadula and W. Veys (Eds.), Bridgind Algebra, Geometry and Topology, Springer Proc. in Math. & Stat., vol. 96 (2014), 249-254; preliminary arXiv version.
  • Every point is critical (with I. Bárány, J. Itoh, and T. Zamfirescu), Adv. Math. 235 (2013), 390-397.
  • Sets of tetrahedra, defined by maxima of distance functions (with J. Rouyer), An. Stiint. Univ. ``Ovidius'' Constanta Ser. Mat. 20 (2012), 197-212.
  • Cut locus structures on graphs (with J. Itoh), Discrete Math. 312 (2012), 524-531; preliminary arXiv version.
  • On the number of cut locus structures on graphs (with J. Itoh), arXiv:1103.1764.
  • Orientable cut locus structures on graphs (with J. Itoh), arXiv:1103.3136.
  • Continuous Flattening of Convex Polyhedra (with J. Itoh and C. Nara), in A. Marquez, P. Ramos and J. Urrutia (Eds.), Computational Geometry, Lecture Notes in Computer Science 7579 (2012), 85-97; abstract in Proc. of the XIV Spanish Meeting on Computational Geometry (EGC2011), Centre de Recerca Matematica (CRM), Documents vol. 8 (2011), 95-98; ISSN 2014-2323.
  • Quasigeodesics and farthest points on convex surfaces (with K. Ieiri and J. Itoh), Adv. Geom. 11 (2011), 571-584.
  • Star unfolding convex polyhedra via quasigeodesic loops (with J. Itoh and J. O'Rourke), Discrete Comput. Geom. 44 (2010), 35-54; preliminary arXiv version; 2-page abstract in Fall Workshop on Computational Geometry 2007, 79-80.
  • Source unfoldings of convex polyhedra with respect to certain closed polygonal curves (with J. Itoh and J. O'Rourke), abstract in Proc. 25th European Workshop Comput. Geom. (EuroCG) 61-64, 2009; arXiv version.
  • Criteria for farthest points on convex surfaces (with J. Itoh), Math. Nachr. 282 (2009), 1537-1547.
  • What do cylinders look like? (with J. Itoh), J. Geom. 95 (2009), 41-48.
  • On typical degenerate convex surfaces, Math. Ann. 340 (2008), 543-567.
  • Common maxima of distance functions on orientable Alexandrov surfaces, J. Math. Soc. Japan 60 (2008), 51-64.
  • Antipodal convex hypersurfaces (with J. Itoh and J. Rouyer), Indag. Math. 19 (2008), 411-426.
  • Multiple farthest points on Alexandrov surfaces (with T. Zamfirescu), Adv. Geom. 7 (2007), 83-100.
  • On the length of simple closed quasigeodesics on convex surfaces (with J. Itoh), C. R. Math. Acad. Sci. Paris Ser. I. 343 (2006), 259-264.
  • Symmetry and the farthest point mapping on convex surfaces (with T. Zamfirescu), Adv. Geom. 6 (2006), 379-387.
  • Properties of the farthest point mapping on convex surfaces, Rev. Roum. Math. Pures Appl. 51 (2006), 125-134. Also published in the volume "Papers on Convexity and Discrete Geometry and other nice fields - Dedicated to Tudor Zamfirescu on the occasion of his 60th birthday", Ed. Academiei Romane, 2006.
  • Farthest points and cut loci on some degenerate convex surfaces (with J. Itoh), J. Geom. 80 (2004), 106-120.
  • On Two Conjectures of Steinhaus, Geom. Dedicata 79 (2000), 267-275.
  • Tangent Bundles and Submanifolds, Bull. Math. Soc. Sci. Math. Roum. 40 (1997), 43-48.
  • On Some Submanifolds of Bochner Flat Indefinite Kaehler Manifolds, in the volume of the Annual Conference of The Romanian Society of Mathematical Sciences, Bucharest 1997, 311-315.
  • An idea from convex geometry (in Romanian), Gazeta Matematica Seria A, Vol. XV 3 (1997), 193-196.