Geodesies on typical convex surfaces
Gruber, Peter Manfred
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 82 (1988), p. 651-659 / Harvested from Biblioteca Digitale Italiana di Matematica

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.

Publié le : 1988-12-01
@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] Alexandrow, A.D. (1955) - Die innere Geometrie konvexer Flächen, Akademie-Verlag, Berlin. | MR 71041 | Zbl 0065.15102

[2] Berger, M. (1987) - Geometry I, Springer, Berlin. | MR 882541

[3] Brauner, H. (1981) - Differentialgeometrie, Vieweg, Braunschweig. | MR 616082 | Zbl 0466.53001

[4] Busemann, H. (1958) - Convex surfaces, Interscience, New York. | MR 105155 | Zbl 0196.55101

[5] Gruber, P.M. (1984) - Aspects of convexity and its applications, Math. Expositions 2 47-83. | MR 783125 | Zbl 0525.52001

[6] Gruber, P.M. (1985) - Results of Baire category type in convexity, Ann. New York Acad. Sci. 440 163-169. | MR 809203 | Zbl 0571.52007

[7] Holmes, R.B. (1985) - Geometric functional analysis and its applications, Springer, New York. | MR 410335 | Zbl 0336.46001

[8] Klingenberg, W. (1978) - Lectures on closed geodesies, Springer, Berlin. | MR 478069 | Zbl 0397.58018

[9] Lusternik, L.A. and Schinirelman, L. G. (1929) - 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

[10] Oxtoby, J.C. (1971) - Measure and category, Springer, New York. | MR 584443

[11] Pogorelov, A.V. (1949) - Quasigeodesics on convex surfaces, Mat. Sb. 25 273-307. | MR 31767

[12] Siegel, C.L. (1975) - Integralfreie Variationsrechnung, Nachr. Akad. Wiss. Göttingen. Math. phys. Kl. 1975 81-86 = Ges. Abh. III, 264-269. | MR 91424 | Zbl 0105.07602

[13] Zamfierescu, T. (1982) - Many endpoints and few interior points of geodesies, Invent. Math. 69 253-257. | MR 674405 | Zbl 0494.52004

[14] Zamfierescu, T. (1985) - Using Baire categories in geometry, Rend. Univ. Politecn. Torino 43 67-88. | MR 859850 | Zbl 0601.52004

[15] Gruber, P.M. (1991) - A typical convex surface contains no closed geodesic, J. Reine Angew. Math., in print. | MR 1099950 | Zbl 0718.52003