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 inProc. 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 inProc. 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 inFall 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 theAnnual 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.