2 citations · 3 across the 7 of their papers we have counts for
4 papers · 1 filter
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…
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…
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…
Asymptotic circularity of immortal area-preserving curvature flows
Tatsuya Miura
For a class of area-preserving curvature flows of closed planar curves, we prove that every immortal solution becomes asymptotically circular without any additional assumptions on…