Using Baire categories uniqueness of geodesic segments and existence of closed geodesics on typical convex surfaces are investigated.
Si investigano problemi delle unicità di segmenti geodetici e della esistenza di linee geodetiche chiuse su superfici convesse che sono tipiche nel senso delle categorie Baire.
@article{RLINA_1988_8_82_4_651_0, author = {Peter Manfred Gruber}, title = {Geodesies on typical convex surfaces}, journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti}, volume = {82}, year = {1988}, pages = {651-659}, zbl = {0741.52006}, mrnumber = {1139812}, language = {en}, url = {http://dml.mathdoc.fr/item/RLINA_1988_8_82_4_651_0} }
Gruber, Peter Manfred. Geodesies on typical convex surfaces. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 82 (1988) pp. 651-659. http://gdmltest.u-ga.fr/item/RLINA_1988_8_82_4_651_0/
[1] | MR 71041 | Zbl 0065.15102
(1955) - Die innere Geometrie konvexer Flächen, Akademie-Verlag, Berlin.[2] | MR 882541
(1987) - Geometry I, Springer, Berlin.[3] | MR 616082 | Zbl 0466.53001
(1981) - Differentialgeometrie, Vieweg, Braunschweig.[4] | MR 105155 | Zbl 0196.55101
(1958) - Convex surfaces, Interscience, New York.[5] Aspects of convexity and its applications, Math. Expositions 2 47-83. | MR 783125 | Zbl 0525.52001
(1984) -[6] Results of Baire category type in convexity, Ann. New York Acad. Sci. 440 163-169. | MR 809203 | Zbl 0571.52007
(1985) -[7] | MR 410335 | Zbl 0336.46001
(1985) - Geometric functional analysis and its applications, Springer, New York.[8] | MR 478069 | Zbl 0397.58018
(1978) - Lectures on closed geodesies, Springer, Berlin.[9] Sur le problème de trois géodesiques fermées sur les surfaces de genre 0, C.R. Acad. Sci. Paris 189 269-271. | JFM 55.0316.02
and (1929) -[10] | MR 584443
(1971) - Measure and category, Springer, New York.[11] Quasigeodesics on convex surfaces, Mat. Sb. 25 273-307. | MR 31767
(1949) -[12] Integralfreie Variationsrechnung, Nachr. Akad. Wiss. Göttingen. Math. phys. Kl. 1975 81-86 = Ges. Abh. III, 264-269. | MR 91424 | Zbl 0105.07602
(1975) -[13] Many endpoints and few interior points of geodesies, Invent. Math. 69 253-257. | MR 674405 | Zbl 0494.52004
(1982) -[14] Using Baire categories in geometry, Rend. Univ. Politecn. Torino 43 67-88. | MR 859850 | Zbl 0601.52004
(1985) -[15] A typical convex surface contains no closed geodesic, J. Reine Angew. Math., in print. | MR 1099950 | Zbl 0718.52003
(1991) -