Add to ORKGOur main point of focus is the set of closed geodesics on hyperbolic surfaces. For any fixed integer $k$, we are interested in the set of all closed geodesics with at least $k$ (but possibly more) self-intersections. Among these, we consider those of minimal length and investigate their self-intersection numbers. We prove that their intersection numbers are upper bounded by a universal linear function in $k$ (which holds for any hyperbolic surface). Moreover, in the presence of cusps, we get bounds which imply that the self-intersection numbers behave asymptotically like $k$ for growing $k$
The leitmotif of this dissertation is the search for length formulas and sharp constants in relation...
Abstract. We classify the free homotopy classes of closed curves with minimal self intersection numb...
Given a hyperbolic surface, the set of all closed geodesics whose length is minimal form a graph on ...
Our main point of focus is the set of closed geodesics on hyperbolic surfaces. For any fixed integer...
AbstractIn this paper, we show that for any hyperbolic surface S, the number of geodesics of length ...
In this thesis, we obtain combinatorial algorithms that determine the minimal number of self-interse...
This note is about a type of quantitative density of closed geodesics on closed hyperbolic surfaces....
For a compact surface $S$ with constant negative curvature $-\kappa$ (for some $\kappa>0$) and genus...
On a hyperbolic Riemann surface, given two simple closed geodesics that intersect n times, we addres...
We prove an upper bound for the number of shortest closed geodesics in a closed hyperbolic manifold...
In this note, we develop a condition on a closed curve on a surface or in a 3-manifold that implies ...
A celebrated result of Mirzakhani states that, if $(S,m)$ is a finite area \emph{orientable} hyperbo...
We classify the free homotopy classes of closed curves with minimal self intersection number two on ...
Let Σ be a closed hyperbolic surface. We study, for fixed g, the asymptotics of the number of those ...
The geometric intersection number of a curve on a surface is the minimal number of self-intersection...
The leitmotif of this dissertation is the search for length formulas and sharp constants in relation...
Abstract. We classify the free homotopy classes of closed curves with minimal self intersection numb...
Given a hyperbolic surface, the set of all closed geodesics whose length is minimal form a graph on ...
Our main point of focus is the set of closed geodesics on hyperbolic surfaces. For any fixed integer...
AbstractIn this paper, we show that for any hyperbolic surface S, the number of geodesics of length ...
In this thesis, we obtain combinatorial algorithms that determine the minimal number of self-interse...
This note is about a type of quantitative density of closed geodesics on closed hyperbolic surfaces....
For a compact surface $S$ with constant negative curvature $-\kappa$ (for some $\kappa>0$) and genus...
On a hyperbolic Riemann surface, given two simple closed geodesics that intersect n times, we addres...
We prove an upper bound for the number of shortest closed geodesics in a closed hyperbolic manifold...
In this note, we develop a condition on a closed curve on a surface or in a 3-manifold that implies ...
A celebrated result of Mirzakhani states that, if $(S,m)$ is a finite area \emph{orientable} hyperbo...
We classify the free homotopy classes of closed curves with minimal self intersection number two on ...
Let Σ be a closed hyperbolic surface. We study, for fixed g, the asymptotics of the number of those ...
The geometric intersection number of a curve on a surface is the minimal number of self-intersection...
The leitmotif of this dissertation is the search for length formulas and sharp constants in relation...
Abstract. We classify the free homotopy classes of closed curves with minimal self intersection numb...
Given a hyperbolic surface, the set of all closed geodesics whose length is minimal form a graph on ...