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Uspekhi Mat. Nauk, 2007, Volume 62, Issue 1(373), Pages 3–50 (Mi umn5589)  

This article is cited in 25 scientific papers (total in 25 papers)

On organizing principles of discrete differential geometry. Geometry of spheres

A. I. Bobenkoa, Yu. B. Surisb

a Institut für Mathematik, Technische Universität Berlin
b Technische Universität München

DOI: https://doi.org/10.4213/rm5589

Full text: PDF file (1021 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2007, 62:1, 1–43

Bibliographic databases:

UDC: 514.15+514.14+514.745.82+514.75
MSC: Primary 53Axx, 51Bxx; Secondary 39A12, 52Cxx
Received: 20.11.2006

Citation: A. I. Bobenko, Yu. B. Suris, “On organizing principles of discrete differential geometry. Geometry of spheres”, Uspekhi Mat. Nauk, 62:1(373) (2007), 3–50; Russian Math. Surveys, 62:1 (2007), 1–43

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Bobenko A.I., Suris Yu.B., “Isothermic surfaces in sphere geometries as Moutard nets”, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 463:2088 (2007), 3171–3193  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Pottmann H., Liu Yang, Wallner J., Bobenko A., Wang Wenping, “Geometry of multi-layer freeform structures for architecture”, Proceedings of ACM SIGGRAPH, 26:3 (2007), 65, 11 pp.  crossref  isi  scopus
    3. Pottmann H., Wallner J., “The focal geometry of circular and conical meshes”, Adv. Comput. Math., 29:3 (2008), 249–268  crossref  mathscinet  zmath  isi  elib  scopus
    4. Bazhanov V.V., Mangazeev V.V., Sergeev S.M., “Quantum geometry of three-dimensional lattices”, J. Stat. Mech. Theory Exp., 2008, no. 7, P07004, 27 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    5. Tsarev S.P., Wolf T., “Classification of three-dimensional integrable scalar discrete equations”, Lett. Math. Phys., 84:1 (2008), 31–39  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. O. I. Mokhov, “On consistency of determinants on cubic lattices”, Russian Math. Surveys, 63:6 (2008), 1146–1148  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. Pottmann H., Grohs Ph., Mitra N.J., “Laguerre minimal surfaces, isotropic geometry and linear elasticity”, Adv. Comput. Math., 31:4 (2009), 391–419  crossref  mathscinet  zmath  isi  scopus
    8. Bobenko A.I., Suris Yu.B., “Discrete Koenigs Nets and Discrete Isothermic Surfaces”, Internat. Math. Res. Notices, 2009, no. 11, 1976–2012  crossref  mathscinet  zmath  isi  scopus
    9. O. I. Mokhov, “Consistency on Cubic Lattices for Determinants of Arbitrary Orders”, Proc. Steklov Inst. Math., 266 (2009), 195–209  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    10. Adler V.E., Suris Yu.B., Bobenko A.I., “Integrable Discrete Nets in Grassmannians”, Lett. Math. Phys., 89:2 (2009), 131–139  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    11. Pottmann H., Grohs Ph., Blaschitz B., “Edge offset meshes in Laguerre geometry”, Adv. Comput. Math., 33:1 (2010), 45–73  crossref  mathscinet  zmath  isi  scopus
    12. Bobenko A.I., Pottmann H., Wallner J., “A curvature theory for discrete surfaces based on mesh parallelity”, Math. Ann., 348:1 (2010), 1–24  crossref  mathscinet  zmath  isi  scopus
    13. Liu ShaoWei, Cheng Yi, He JingSong, “The determinant representation of the gauge transformation for the discrete KP hierarchy”, Sci. China Math., 53:5 (2010), 1195–1206  crossref  mathscinet  zmath  isi  elib  scopus
    14. Bazhanov V.V., Mangazeev V.V., Sergeev S.M., “Quantum geometry of 3-dimensional lattices and tetrahedron equation”, Xvith International Congress on Mathematical Physics, World Sci. Publ., Hackensack, NJ, 2010, 23–44  crossref  mathscinet  zmath  isi  scopus
    15. Oleg I. Mokhov, “On Initial Data in the Problem of Consistency on Cubic Lattices for $3\times3$ Determinants”, SIGMA, 7 (2011), 075, 19 pp.  mathnet  crossref  mathscinet
    16. Bobenko A.I., Huhnen-Venedey E., “Curvature line parametrized surfaces and orthogonal coordinate systems: discretization with Dupin cyclides”, Geom. Dedicata, 159:1 (2012), 207–237  crossref  mathscinet  zmath  isi  elib  scopus
    17. Skopenkov M., Pottmann H., Grohs Ph., “Ruled Laguerre minimal surfaces”, Math. Z., 272:1-2 (2012), 645–674  crossref  mathscinet  zmath  isi  scopus
    18. Wallner J., “On the semidiscrete differential geometry of A-surfaces and K-surfaces”, J. Geom., 103:1 (2012), 161–176  crossref  mathscinet  zmath  scopus
    19. Huhnen-Venedey E., Rörig Th., “Discretization of asymptotic line parametrizations using hyperboloid surface patches”, Geom. Dedicata, 2013  crossref  mathscinet  isi  scopus
    20. George Shapiro, “On discrete differential geometry in twistor space”, Journal of Geometry and Physics, 2013  crossref  mathscinet  isi  scopus
    21. Burstall F., Hertrich-Jeromin U., Mueller C., Rossman W., “Semi-discrete isothermic surfaces”, Geod. Dedic., 183:1 (2016), 43–58  crossref  mathscinet  zmath  isi  scopus
    22. Musso E., Nicolodi L., “Holomorphic differentials and Laguerre deformation of surfaces”, Math. Z., 284:3-4 (2016), 1089–1110  crossref  mathscinet  zmath  isi  elib  scopus
    23. Colapinto P., “Composing Surfaces with Conformal Rotors”, Adv. Appl. Clifford Algebr., 27:1, SI (2017), 453–474  crossref  mathscinet  zmath  isi  scopus
    24. Ulrych S., “Holographic Coordinates”, J. Math. Anal. Appl., 465:2 (2018), 1056–1074  crossref  mathscinet  zmath  isi  scopus
    25. Lam W.Y., “Discrete Minimal Surfaces: Critical Points of the Area Functional From Integrable Systems”, Int. Math. Res. Notices, 2018, no. 6, 1808–1845  crossref  mathscinet  isi  scopus
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