Answer by Pengfei for Which surfaces admit unbounded-length simple geodesics?
Anosov constructed (Anosov, Section 8) a smooth Riemannian metric $g$ on $S^2$ such that the surface $(S^2,g)$ admits arbitrarily long non-intersecting closed geodesics. His construction starts with a...
View ArticleAnswer by Vladimir S Matveev for Which surfaces admit unbounded-length simple...
Elipsoid does not posess unbounded geodesics with no self-intersection. I do not know a conceptual explanation. My explanation is that (due to integrability of the geodesic flow of ellipsoid) we know...
View ArticleAnswer by Igor Rivin for Which surfaces admit unbounded-length simple geodesics?
This paperRouyer, Joël(R-AOS); Vîlcu, Costin(R-AOS)Simple closed geodesics on most Alexandrov surfaces. (English summary) Adv. Math. 278 (2015), 103–120. 53C45 (53C22) Indicates that this is usually...
View ArticleWhich surfaces admit unbounded-length simple geodesics?
Let $S$ be a surface embedded in $\mathbb{R}^3$.A simple geodesic on $S$ is one that does not self-intersect.Some surfaces have simple geodesics whose length exceeds anygiven bound $L$. For example, a...
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