6 citations · 29 across the 16 of their papers we have counts for
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Simple closed geodesics on most Alexandrov surfaces
Joël Rouyer, Costin Vîlcu
We study the existence of simple closed geodesics on most (in the sense of Baire category) Alexandrov surfaces with curvature bounded below, compact and without boundary. We show t…
The connected components of the space of Alexandrov surfaces
Joël Rouyer, Costin Vîlcu
Denote by the set of all compact Alexandrov surfaces with curvature bounded below by without boundary, endowed with the topology induced by the Gromov-Hausdorf…
Moderate smoothness of most Alexandrov surfaces
Jin-ichi Itoh, Joel Rouyer, Costin Vilcu
We show that, in the sense of Baire category, most Alexandrov surfaces with curvature bounded below by have no conical points. We use this result to prove that at most points o…
On the Theorem of the Three Perpendiculars
Jin-ichi Itoh, Joel Rouyer, Costin Vilcu
We show that the theorem of the three perpendiculars holds in any n-dimensional space form.