no. 1
Variational properties of the discrete Hilbert-Einstein functional
Izmestiev, Ivan1
1 Institut für Mathematik, Freie Universität Berlin, Arnimallee 2, 14195 Berlin
Actes des rencontres du CIRM, Tome 3 (2013) no. 1, pp. 151-157.
Publié le :
DOI : 10.5802/acirm.64
Izmestiev, Ivan 1

1 Institut für Mathematik, Freie Universität Berlin, Arnimallee 2, 14195 Berlin 
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Izmestiev, Ivan. Variational properties of the discrete Hilbert-Einstein functional. Actes des rencontres du CIRM, Tome 3 (2013) no. 1, pp. 151-157. doi : 10.5802/acirm.64. http://www.numdam.org/articles/10.5802/acirm.64/

[1] Alexandrov, Alexander D. Existence of a convex polyhedron and of a convex surface with a given metric, Mat. Sbornik, N. Ser., Volume 11(53) (1942), pp. 15-65 (Russian. English summary)

[2] Anderson, Michael T. Scalar curvature and the existence of geometric structures on 3-manifolds. I, J. Reine Angew. Math., Volume 553 (2002), pp. 125-182 | DOI | MR | Zbl

[3] Anderson, Michael T. Scalar curvature and the existence of geometric structures on 3-manifolds. II, J. Reine Angew. Math., Volume 563 (2003), pp. 115-195 | DOI | MR | Zbl

[4] Besse, Arthur L. Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 10, Springer-Verlag, Berlin, 1987, xii+510 pages | MR | Zbl

[5] Blaschke, Wilhelm; Herglotz, Gustav Über die Verwirklichung einer geschlossenen Fläche mit vorgeschriebenem Bogenelement im Euklidischen Raum, Sitzungsber. Bayer. Akad. Wiss., Math.-Naturwiss. Abt., Volume No.2 (1937), pp. 229-230 | Zbl

[6] Bobenko, Alexander I.; Izmestiev, Ivan Alexandrov’s theorem, weighted Delaunay triangulations, and mixed volumes, Ann. Inst. Fourier (Grenoble), Volume 58 (2008) no. 2, pp. 447-505 | DOI | Numdam | MR | Zbl

[7] Calabi, Eugenio On compact, Riemannian manifolds with constant curvature. I, Proc. Sympos. Pure Math., Vol. III, American Mathematical Society, Providence, R.I., 1961, pp. 155-180 | DOI | Zbl

[8] Cheeger, Jeff; Müller, Werner; Schrader, Robert On the curvature of piecewise flat spaces, Comm. Math. Phys., Volume 92 (1984) no. 3, pp. 405-454 | DOI | MR | Zbl

[9] Cooper, Daryl; Rivin, Igor Combinatorial scalar curvature and rigidity of ball packings, Math. Res. Lett., Volume 3 (1996) no. 1, pp. 51-60 | DOI | MR | Zbl

[10] Fillastre, François; Izmestiev, Ivan Hyperbolic cusps with convex polyhedral boundary, Geom. Topol., Volume 13 (2009) no. 1, pp. 457-492 | DOI | MR | Zbl

[11] Glickenstein, David Discrete conformal variations and scalar curvature on piecewise flat two- and three-dimensional manifolds, J. Differential Geom., Volume 87 (2011) no. 2, pp. 201-237 http://projecteuclid.org/getRecord?id=euclid.jdg/1304514973 | MR | Zbl

[12] Izmestiev, Ivan The Colin de Verdière number and graphs of polytopes, Israel J. Math., Volume 178 (2010), pp. 427-444 | DOI | MR | Zbl

[13] Izmestiev, Ivan Examples of infinitesimally flexible 3–dimensional hyperbolic cone-manifolds, J. Math. Soc. Japan, Volume 63 (2011) no. 2, pp. 581-598 | MR | Zbl

[14] Izmestiev, Ivan Infinitesimal rigidity of convex polyhedra through the second derivative of the Hilbert-Einstein functional, Canad. J. Math., Volume 66 (2014) no. 4, pp. 783-825 | DOI | MR | Zbl

[15] Izmestiev, Ivan; Schlenker, Jean-Marc Infinitesimal rigidity of polyhedra with vertices in convex position, Pacific J. Math., Volume 248 (2010) no. 1, pp. 171-190 | DOI | MR | Zbl

[16] Koiso, Norihito Nondeformability of Einstein metrics, Osaka J. Math., Volume 15 (1978) no. 2, pp. 419-433 http://projecteuclid.org/getRecord?id=euclid.ojm/1200771282 | MR | Zbl

[17] Mazzeo, Rafe; Montcouquiol, Grégoire Infinitesimal rigidity of cone-manifolds and the Stoker problem for hyperbolic and Euclidean polyhedra, J. Differential Geom., Volume 87 (2011) no. 3, pp. 525-576 http://projecteuclid.org/getRecord?id=euclid.jdg/1312998235 | MR | Zbl

[18] Regge, Tullio General relativity without coordinates, Nuovo Cimento, Volume 19 (1961), pp. 558-571 | DOI | MR

[19] Sechelmann, Stefan Alexandrov’s Polyhedron Editor, Java Web Start application (http://page.math.tu-berlin.de/ sechel/webstart/AlexandrovPolyhedron.jnlp)

[20] Weil, André On discrete subgroups of Lie groups, Ann. of Math. (2), Volume 72 (1960), pp. 369-384 | DOI | MR

[21] Weiss, Hartmut The deformation theory of hyperbolic cone-3-manifolds with cone-angles less than 2π, Geom. Topol., Volume 17 (2013), 329–367 pages | MR | Zbl

[22] Yamabe, Hidehiko On a deformation of Riemannian structures on compact manifolds, Osaka Math. J., Volume 12 (1960), pp. 21-37 | MR | Zbl

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