Minimal area surfaces and fibered hyperbolic $3$-manifolds

James Farre; Franco Vargas Pallete

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arXiv · 2105.02631

Minimal area surfaces and fibered hyperbolic $3$-manifolds

James Farre·Franco Vargas Pallete

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Abstract

By work of Uhlenbeck, the largest principal curvature of any least area fiber of a hyperbolic $3$-manifold fibering over the circle is bounded below by one. We give a short argument to show that, along certain families of fibered hyperbolic $3$-manifolds, there is a uniform lower bound for the maximum principal curvatures of a least area minimal surface which is greater than one.

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James Farre, Franco Vargas Pallete. 2021-05-06. Minimal area surfaces and fibered hyperbolic $3$-manifolds. https://arxiv.org/abs/2105.02631

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