5 citations · 11 across the 9 of their papers we have counts for
9 papers
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…
Upper and lower bounds and modulus of continuity of decomposed Möbius energies
Aya Ishizeki, Takeyuki Nagasawa
The Möbius energy is one of the knot energies, and is named after its Möbius invariant property. It is known to have several different expressions. One is in terms of the cosine of…
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…
Cosine formula for generalized O'Hara's energies
Takeyuki Nagasawa
In this short article, we extend the cosine formula for the Möbius energy to generalized O'Hara energies. The newly derived formula gives us a condition for which the right circle…
A Möbius invariant discretization and decomposition of the Möbius energy
Simon Blatt, Aya Ishizeki, Takeyuki Nagasawa
The Möbius energy, defined by O'Hara, is one of the knot energies, and named after the Möbius invariant property which was shown by Freedman-He-Wang. The energy can be decomposed i…
Decomposition of generalized O'Hara's energies
Aya Ishizeki, Takeyuki Nagasawa
O'Hara introduced several functionals as knot energies. One of them is the Möbius energy. We know its Möbius invariance from Doyle-Schramm's cosine formula. It is also known that t…
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…
A Möbius invariant discretization of O'Hara's Möbius energy
Simon Blatt, Aya Ishizeki, Takeyuki Nagasawa
We introduce a new discretization of O'Hara's Möbius energy. In contrast to the known discretizations of Simon and Kim and Kusner it is invariant under Möbius transformations of th…
On the global existence of generalized rotational hypersurfaces with prescribed mean curvature in the Euclidean spaces, II
Takeyuki Nagasawa
In the previous paper, it has been proved that the generalized rotational hypersurfaces of O(n-1)-type and O (l+1) x O(m+1)-type, for which the mean curvature is any prescribed con…