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math.DG2026
Topping's diameter conjecture for immersed surfaces
Tatsuya Miura
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 sh…
math.DG2026
The elastic figure-eight knot is not planar
Tatsuya Miura
We prove that every elastic knot in any non-torus twist knot class is not planar. In particular, this disproves a numerically motivated planarity conjecture for elastic figure-eigh…
math.DG2026
Milnor's inequality and circular elastic knots
Tatsuya Miura
We establish the extension of Milnor's inequality, relating total curvature with the bridge index, to the -closure of a knot class, without any restriction on the self-interse…