Thursday 11 June 2015 from 15:00–16:00 in Carslaw 535A

Minimal surfaces in hyperbolic 3-manifolds

Hyam Rubinstein (Melbourne)


Minimal surfaces played a key role in the development of 3-manifold topology in the early 1980s with work of Freedman, Hass, Meeks, Schoen, Scott, Simon and Yau. Recently there has been a resurgence of interest in the connection between minimal surfaces and hyperbolic metrics. A quick survey will be given of basic existence results and then two specific problems will be discussed. One is the relation between large (Margulis) tubes around short geodesic loops and multiple minimal surfaces in the same isotopy class. The other is a combinatorial analogue of surfaces with small principal curvature (almost Fuchsian surfaces), which were crucial in breakthrough work of Kahn, Markovic and Agol.

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