Max Neumann-Coto
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Taut smoothings of arcs and curves Open
We study the geometric and combinatorial effect of smoothing an intersection point in a collection of arcs or curves on a surface. We prove that all taut arcs with fixed endpoints and all taut 1-manifolds with at least two non-disjoint com…
A property of closed geodesics on hyperbolic surfaces Open
We study closed geodesics on hyperbolic surfaces and give bounds for their angles of intersection and self-intersection, as well as for the size of the n -gons that they form, depending only on the lengths of the geodesics.
A geometric property of closed geodesics on hyperbolic surfaces Open
We study closed geodesics on hyperbolic surfaces, and give bounds for their angles of intersection and self-intersection, and for the sides of the polygons that they form, depending only on the lengths of the geodesics
Measuring complexity of curves on surfaces Open
We consider the relations between different measures of complexity for free homotopy classes of curves on a surface $Σ$, including the minimum number of self-intersections, the minimum length of the words representing them in a geometric p…