@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}, pages = {213--219}, publisher = {Seminario Matematico of the University of Padua}, volume = {98}, year = {1997}, mrnumber = {1492978}, zbl = {0897.53003}, language = {en}, url = {http://www.numdam.org/item/RSMUP_1997__98__213_0/} }
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 SP - 213 EP - 219 VL - 98 PB - Seminario Matematico of the University of Padua UR - http://www.numdam.org/item/RSMUP_1997__98__213_0/ LA - en ID - RSMUP_1997__98__213_0 ER -
%0 Journal Article %A Gutierrez, Carlos %A Sánchez-Bringas, Federico %T On a Carathéodory's conjecture on umbilics : representing ovaloids %J Rendiconti del Seminario Matematico della Università di Padova %D 1997 %P 213-219 %V 98 %I Seminario Matematico of the University of Padua %U http://www.numdam.org/item/RSMUP_1997__98__213_0/ %G en %F 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, Volume 98 (1997), pp. 213-219. http://www.numdam.org/item/RSMUP_1997__98__213_0/
[Bol] Über Nabelpunkte auf einer Eifläche, Math. Z., 49 (1943/1944), pp. 389-410. | MR | Zbl
,[GMS] On a Carathéodoryś Conjecture: analyticity versus smoothness, To appear in Experimental Mathematics. | Zbl
- - ,[Fav] Sur la determination des surfaces convexes, Bull. Acad. Roy. Belgique, 19 (1933), pp. 65-75. | Zbl
,[Fir] The determination of convex bodies from their mean radius of curvature functions, Mathematika, 14 (1967), pp. 1-13. | MR | Zbl
,[Ham] Beweis einer Carathéodoryschen Vermütung, Ann. Math., 41 (1940), pp. 63-68; II, III, Acta Math., 73 (1941), pp. 174-332. | JFM
,[Hop] Differential Geometry in the Large, Lecture Notes, 1000, Springer-Verlag (1989). | MR | Zbl
,[Klo] On Bol's proof of Carathéodory's Conjecture, Comm. Pure Appl. Math., 12 (1959), pp. 277-311. | MR | Zbl
,[Lan] Nabelpunkte, Krümmungslinien, Brennflächen und ihre Metamorphosen, Dissertation, Technische Hochschule Darmstadt, Darmstadt (1990). | Zbl
,[Nir] The Weyl-Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math., 6 (1953), pp. 337-394. | MR | Zbl
,[Sch] A new proof of Hamburger's Index Theorem on umbilical points, Dissertation ETH No. 10281.
,[Tit] A proof of a conjecture of Loewner and of the conjecture of Carathéodory on umbilic points, Acta Math., 131 (1973), pp. 43-77. | MR | Zbl
,[Yau] Seminar on Differential Geometry, Princenton University Press, Princenton, New Jersey (1982). | MR | Zbl
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