Topping's diameter conjecture for immersed surfaces
Tatsuya Miura
Abstract
We resolve Topping's diameter conjecture for closed immersed surfaces in Euclidean three-space, building on his recent result for embedded surfaces. More generally, we establish sharp diameter and mean-width estimates for compact connected immersed surfaces, possibly with boundary. As a consequence, we confirm the codimension-one case of the sharp length--diameter conjecture for immersed minimal surfaces.
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