Answer by Benoît Kloeckner for Is there a unified reason that there are an...
It seems to me that one could design a dynamical unified argument. The following might be turned into a proof, but there are some points to check.Let $x,y$ be your two non-conjugate points, and let $v$...
View ArticleAnswer by Renato G. Bettiol for Is there a unified reason that there are an...
It seems to me that the OP's last remarks about the difference of the cases when $\pi_1(M)$ is finite or infinite already give the answer to the question. Namely, the two cases are not that different,...
View ArticleIs there a unified reason that there are an infinite number of geodesics...
The proof of this statement seems to break into two really different arguments. So, I'm wondering if there is a better argument that can explain them both, or whether it's really just two theorems that...
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