On a Carathéodory's conjecture on umbilics : representing ovaloids

Carlos Gutierrez; Federico Sánchez-Bringas

Rendiconti del Seminario Matematico della Università di Padova (1997)

  • Volume: 98, page 213-219
  • ISSN: 0041-8994

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Gutierrez, Carlos, and Sánchez-Bringas, Federico. "On a Carathéodory's conjecture on umbilics : representing ovaloids." Rendiconti del Seminario Matematico della Università di Padova 98 (1997): 213-219. <http://eudml.org/doc/108443>.

@article{Gutierrez1997,
author = {Gutierrez, Carlos, Sánchez-Bringas, Federico},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {stereographic projection; Carathéodory’s conjecture; umbilics; representations of ovaloids; Bonnet chart; curvature lines; support function},
language = {eng},
pages = {213-219},
publisher = {Seminario Matematico of the University of Padua},
title = {On a Carathéodory's conjecture on umbilics : representing ovaloids},
url = {http://eudml.org/doc/108443},
volume = {98},
year = {1997},
}

TY - JOUR
AU - Gutierrez, Carlos
AU - Sánchez-Bringas, Federico
TI - On a Carathéodory's conjecture on umbilics : representing ovaloids
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1997
PB - Seminario Matematico of the University of Padua
VL - 98
SP - 213
EP - 219
LA - eng
KW - stereographic projection; Carathéodory’s conjecture; umbilics; representations of ovaloids; Bonnet chart; curvature lines; support function
UR - http://eudml.org/doc/108443
ER -

References

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  1. [Bol] G. Bol, Über Nabelpunkte auf einer Eifläche, Math. Z., 49 (1943/1944), pp. 389-410. Zbl0028.42501MR12489
  2. [GMS] C. Gutierrez - F. Mercury - F. Sánchez-Bringas, On a Carathéodoryś Conjecture: analyticity versus smoothness, To appear in Experimental Mathematics. Zbl0862.57023
  3. [Fav] J. Favard, Sur la determination des surfaces convexes, Bull. Acad. Roy. Belgique, 19 (1933), pp. 65-75. Zbl0007.35902
  4. [Fir] W.J. Firey, The determination of convex bodies from their mean radius of curvature functions, Mathematika, 14 (1967), pp. 1-13. Zbl0161.19302MR217699
  5. [Ham] H. Hamburguer, Beweis einer Carathéodoryschen Vermütung, Ann. Math., 41 (1940), pp. 63-68; II, III, Acta Math., 73 (1941), pp. 174-332. Zbl0023.06902JFM67.0696.01
  6. [Hop] H. Hopf, Differential Geometry in the Large, Lecture Notes, 1000, Springer-Verlag (1989). Zbl0669.53001MR1013786
  7. [Klo] T. Klotz, On Bol's proof of Carathéodory's Conjecture, Comm. Pure Appl. Math., 12 (1959), pp. 277-311. Zbl0091.34301MR120602
  8. [Lan] M. Lang, Nabelpunkte, Krümmungslinien, Brennflächen und ihre Metamorphosen, Dissertation, Technische HochschuleDarmstadt, Darmstadt (1990). Zbl0722.53002
  9. [Nir] Nirenberg, The Weyl-Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math., 6 (1953), pp. 337-394. Zbl0051.12402MR58265
  10. [Sch] H. Scherbel, A new proof of Hamburger's Index Theorem on umbilical points, Dissertation ETH No. 10281. 
  11. [Tit] C.J. Titus, A proof of a conjecture of Loewner and of the conjecture of Carathéodory on umbilic points, Acta Math., 131 (1973), pp. 43-77. Zbl0301.53001MR415543
  12. [Yau] Yau S.T., Seminar on Differential Geometry, Princenton University Press, Princenton, New Jersey (1982). Zbl0471.00020MR645728

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