On a Carathéodory's conjecture on umbilics : representing ovaloids
Gutierrez, Carlos ; Sánchez-Bringas, Federico
Rendiconti del Seminario Matematico della Università di Padova, Tome 98 (1997), p. 213-219 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1997-01-01
@article{RSMUP_1997__98__213_0,
     author = {Gutierrez, Carlos and S\'anchez-Bringas, Federico},
     title = {On a Carath\'eodory's conjecture on umbilics : representing ovaloids},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {98},
     year = {1997},
     pages = {213-219},
     mrnumber = {1492978},
     zbl = {0897.53003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_1997__98__213_0}
}

Gutierrez, Carlos; Sánchez-Bringas, Federico. On a Carathéodory's conjecture on umbilics : representing ovaloids. Rendiconti del Seminario Matematico della Università di Padova, Tome 98 (1997) pp. 213-219. http://gdmltest.u-ga.fr/item/RSMUP_1997__98__213_0/

[Bol] G. Bol, Über Nabelpunkte auf einer Eifläche, Math. Z., 49 (1943/1944), pp. 389-410. | MR 12489 | Zbl 0028.42501

[GMS] C. Gutierrez - F. Mercury - F. Sánchez-Bringas, On a Carathéodoryś Conjecture: analyticity versus smoothness, To appear in Experimental Mathematics. | Zbl 0862.57023

[Fav] J. Favard, Sur la determination des surfaces convexes, Bull. Acad. Roy. Belgique, 19 (1933), pp. 65-75. | Zbl 0007.35902

[Fir] W.J. Firey, The determination of convex bodies from their mean radius of curvature functions, Mathematika, 14 (1967), pp. 1-13. | MR 217699 | Zbl 0161.19302

[Ham] H. Hamburguer, Beweis einer Carathéodoryschen Vermütung, Ann. Math., 41 (1940), pp. 63-68; II, III, Acta Math., 73 (1941), pp. 174-332. | JFM 67.0696.01

[Hop] H. Hopf, Differential Geometry in the Large, Lecture Notes, 1000, Springer-Verlag (1989). | MR 1013786 | Zbl 0669.53001

[Klo] T. Klotz, On Bol's proof of Carathéodory's Conjecture, Comm. Pure Appl. Math., 12 (1959), pp. 277-311. | MR 120602 | Zbl 0091.34301

[Lan] M. Lang, Nabelpunkte, Krümmungslinien, Brennflächen und ihre Metamorphosen, Dissertation, Technische Hochschule Darmstadt, Darmstadt (1990). | Zbl 0722.53002

[Nir] Nirenberg, The Weyl-Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math., 6 (1953), pp. 337-394. | MR 58265 | Zbl 0051.12402

[Sch] H. Scherbel, A new proof of Hamburger's Index Theorem on umbilical points, Dissertation ETH No. 10281.

[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. | MR 415543 | Zbl 0301.53001

[Yau] Yau S.T., Seminar on Differential Geometry, Princenton University Press, Princenton, New Jersey (1982). | MR 645728 | Zbl 0471.00020