Metrics without Morse index bounds
Colding, Tobias H. ; Hingston, Nancy
Duke Math. J., Tome 120 (2003) no. 3, p. 345-365 / Harvested from Project Euclid
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On any surface we give an example of a metric that contains simple closed geodesics with arbitrarily high Morse index. Similarly, on any $3$-manifold we give an example of a metric that contains embedded minimal tori with arbitrarily high Morse index. Previously, no such examples were known. We also discuss whether or not such bounds should hold for a generic metric and why bumpy does not seem to be the right generic notion. Finally, we mention briefly what such bounds might be used for.ADDHERE
Publié le : 2003-08-15
Classification:  58E10,  53C22 
@article{1082744735,
     author = {Colding, Tobias H. and Hingston, Nancy},
     title = {Metrics without Morse index bounds},
     journal = {Duke Math. J.},
     volume = {120},
     number = {3},
     year = {2003},
     pages = { 345-365},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1082744735}
}

Colding, Tobias H.; Hingston, Nancy. Metrics without Morse index bounds. Duke Math. J., Tome 120 (2003) no. 3, pp.  345-365. http://gdmltest.u-ga.fr/item/1082744735/