2 citations · 3 across the 7 of their papers we have counts for
9 papers
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…
Phase transition thresholds and chiral magnetic fields of general degree
Slim Ibrahim, Tatsuya Miura, Carlos Román +1
We study a variational problem for the Landau--Lifshitz energy with Dzyaloshinskii--Moriya interactions arising in 2D micromagnetics, focusing on the Bogomol'nyi regime. We first d…
Regularity and structure of non-planar -elasticae
Florian Gruen, Tatsuya Miura
We prove regularity and structure results for -elasticae in , with arbitrary and . Planar -elasticae are already classified and known…
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…
Migrating elastic flows II
Tatsuya Miura
We solve a variant of Huisken's problem for open curves: we construct migrating elastic flows under the natural boundary conditions, extending previous work from the nonlocal flow…
Smooth compactness of elasticae
Tatsuya Miura
We prove a smooth compactness theorem for the space of elasticae, unless the limit curve is a straight segment. As an application, we obtain smooth stability results for minimizers…
Elastic curves and self-intersections
Tatsuya Miura
This is an expository note to give a brief review of classical elastica theory, mainly prepared for giving a more detailed proof of the author's Li--Yau type inequality for self-in…