Geodesies on typical convex surfaces

Peter Manfred Gruber

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1988)

  • Volume: 82, Issue: 4, page 651-659
  • ISSN: 0392-7881

Abstract

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Using Baire categories uniqueness of geodesic segments and existence of closed geodesics on typical convex surfaces are investigated.

How to cite

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Gruber, Peter Manfred. "Geodesies on typical convex surfaces." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 82.4 (1988): 651-659. <http://eudml.org/doc/289062>.

@article{Gruber1988,
abstract = {Using Baire categories uniqueness of geodesic segments and existence of closed geodesics on typical convex surfaces are investigated.},
author = {Gruber, Peter Manfred},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
keywords = {Convex surfaces; Geodesies; Uniqueness of geodesic segments; Closed geodesies},
language = {eng},
month = {12},
number = {4},
pages = {651-659},
publisher = {Accademia Nazionale dei Lincei},
title = {Geodesies on typical convex surfaces},
url = {http://eudml.org/doc/289062},
volume = {82},
year = {1988},
}

TY - JOUR
AU - Gruber, Peter Manfred
TI - Geodesies on typical convex surfaces
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1988/12//
PB - Accademia Nazionale dei Lincei
VL - 82
IS - 4
SP - 651
EP - 659
AB - Using Baire categories uniqueness of geodesic segments and existence of closed geodesics on typical convex surfaces are investigated.
LA - eng
KW - Convex surfaces; Geodesies; Uniqueness of geodesic segments; Closed geodesies
UR - http://eudml.org/doc/289062
ER -

References

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  1. ALEXANDROW, A.D. (1955) - Die innere Geometrie konvexer Flächen, Akademie-Verlag, Berlin. Zbl0065.15102MR71041
  2. BERGER, M. (1987) - Geometry I, Springer, Berlin. MR882541DOI10.1007/978-3-540-93815-6
  3. BRAUNER, H. (1981) - Differentialgeometrie, Vieweg, Braunschweig. Zbl0466.53001MR616082
  4. BUSEMANN, H. (1958) - Convex surfaces, Interscience, New York. Zbl0196.55101MR105155
  5. GRUBER, P.M. (1984) - Aspects of convexity and its applications, Math. Expositions247-83. Zbl0525.52001MR783125
  6. GRUBER, P.M. (1985) - Results of Baire category type in convexity, Ann. New York Acad. Sci.440163-169. Zbl0571.52007MR809203DOI10.1111/j.1749-6632.1985.tb14550.x
  7. HOLMES, R.B. (1985) - Geometric functional analysis and its applications, Springer, New York. Zbl0336.46001MR410335
  8. KLINGENBERG, W. (1978) - Lectures on closed geodesies, Springer, Berlin. Zbl0397.58018MR478069
  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. Paris189269-271. JFM55.0316.02
  10. OXTOBY, J.C. (1971) - Measure and category, Springer, New York. MR584443
  11. POGORELOV, A.V. (1949) - Quasigeodesics on convex surfaces, Mat. Sb.25273-307. MR31767
  12. SIEGEL, C.L. (1975) - Integralfreie Variationsrechnung, Nachr. Akad. Wiss. Göttingen. Math. phys. Kl. 197581-86 = Ges. Abh. III, 264-269. Zbl0105.07602MR91424
  13. ZAMFIERESCU, T. (1982) - Many endpoints and few interior points of geodesies, Invent. Math.69253-257. Zbl0494.52004MR674405DOI10.1007/BF01399505
  14. ZAMFIERESCU, T. (1985) - Using Baire categories in geometry, Rend. Univ. Politecn. Torino4367-88. Zbl0601.52004MR859850
  15. GRUBER, P.M. (1991) - A typical convex surface contains no closed geodesic, J. Reine Angew. Math., in print. Zbl0718.52003MR1099950DOI10.1515/crll.1991.416.195

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