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6 votes

Is there the longest geodesic?

No such bound $C(\gamma)$ exists, even when $S$ is the two-sphere and even assuming that all geodesics considered are simple. Here is the example (which generalises to surfaces with genus). Suppose t …
Sam Nead's user avatar
  • 28.1k
2 votes
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Pair of laminations that fill on a closed surface

The answer is "no". For consider the case where $L_1 = L_2$ is a single simple closed geodesic. Now you've added the hypothesis that $L_1$ and $L_2$ have no common leaf, the answer becomes "yes". H …
Sam Nead's user avatar
  • 28.1k