On a conjecture of Carathéodory: analyticity versus smoothness
Gutierrez, Carlos ; Mercuri, Francesco ; Sánchez-Bringas, Federico
Experiment. Math., Tome 5 (1996) no. 4, p. 33-37 / Harvested from Project Euclid
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We show that, under mild nonflatness conditions, for any $r\ge 3$ and any $C^r$-immersion of a surface into $\R^3$ with an isolated umbilic point there exist an analytic surface with an isolated umbilic of the same index. The connection of this with Carathéodory's Conjecture on umbilics is discussed.
Publié le : 1996-05-14
Classification:  53A05 
@article{1047591145,
     author = {Gutierrez, Carlos and Mercuri, Francesco and S\'anchez-Bringas, Federico},
     title = {On a conjecture of Carath\'eodory: analyticity versus smoothness},
     journal = {Experiment. Math.},
     volume = {5},
     number = {4},
     year = {1996},
     pages = { 33-37},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1047591145}
}

Gutierrez, Carlos; Mercuri, Francesco; Sánchez-Bringas, Federico. On a conjecture of Carathéodory: analyticity versus smoothness. Experiment. Math., Tome 5 (1996) no. 4, pp.  33-37. http://gdmltest.u-ga.fr/item/1047591145/