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Youngju Kim, Tubular Neighborhoods in Complex Hyperbolic Manifolds
February 7 @ 4:00 pm - 5:00 pm KST
The collar lemma says that a closed geodesic in a real hyperbolic 2-manifold has an embedded tubular neighborhood whose width only depends on the length of the geodesic. The width of the collar does not depend on the underlying hyperbolic 2-manifold. On the other hand, a totally geodesic surface with codimension bigger than 1 in a hyperbolic manifold of can be arbitrary closed to itself. Here, we prove that an embedded complex totally geodesic surface in a complex hyperbolic 2-manifold has a tubular neighborhood whose size depends only on its area. This is a joint work with A. Basmajian.