Timeline for Which surfaces admit unbounded-length simple geodesics?
Current License: CC BY-SA 3.0
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| Nov 13, 2015 at 8:47 | history | edited | Vladimir S Matveev | CC BY-SA 3.0 |
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| Nov 13, 2015 at 8:45 | comment | added | Vladimir S Matveev | I do not understand the question, Joseph (and would love if you give more details) but let me still try. I understood your question such that your ''going to be a counterexample'' curve stays from from one side of some closed geodesic and is closer and closer to it for big times. Then, one may think that your ''going to be a counterexample'' lies on a variation of your closed geodesic, i.e., is controlled by Jacobi vector field. By Jacobi vector field is controlled by the equation involving curvature and for positive curvatur it vanishes in finite time so something goes wrong | |
| Nov 13, 2015 at 5:48 | comment | added | Joseph O'Rourke | Thank you! I do not doubt your proof for a second. But is there any intuition that can help explain why a very nearly closed geodesic around the minor axis of the ellipsoid does not wind around near that closed geodesic many times before self-intersecting? | |
| Nov 12, 2015 at 17:38 | history | edited | Vladimir S Matveev | CC BY-SA 3.0 |
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| Nov 12, 2015 at 16:01 | history | answered | Vladimir S Matveev | CC BY-SA 3.0 |