2 citations · 3 across the 7 of their papers we have counts for
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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…