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math.AP2020
Asymptotic analysis for non-local curvature flows for plane curves with a general rotation number
Takeyuki Nagasawa, Kohei Nakamura
Several non-local curvature flows for plane curves with a general rotation number are discussed in this work. The types of flows include the area-preserving flow and the length-pre…
math.AP2019
Variational formulae and estimates of O'Hara's knot energies
Shoya Kawakami, Takeyuki Nagasawa
O'Hara's energies, introduced by Jun O'Hara, were proposed to answer the question of what is the canonical shape in a given knot type, and were configured so that the less the ener…
math.AP2018
Interpolation inequalities between the deviation of curvature and the isoperimetric ratio with applications to geometric flows
Takeyuki Nagasawa, Kohei Nakamura
Several inequalities for the isoperimetric ratio for plane curves are derived. In particular, we obtain interpolation inequalities between the deviation of curvature and the isoper…