Zobrazeno 1 - 10
of 38
pro vyhledávání: '"Takeyuki Nagasawa"'
Autor:
Takeyuki Nagasawa, Kohei Nakamura
Publikováno v:
Mathematics in Engineering, Vol 3, Iss 6, Pp 1-26 (2021)
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-preserving flow. We have a relatively good understanding of these flows f
Externí odkaz:
https://doaj.org/article/3b550bfe51474498a67ed59d43824cfb
Autor:
Kohei Nakamura, Takeyuki Nagasawa
Publikováno v:
Mathematics in Engineering, Vol 3, Iss 6, Pp 1-26 (2021)
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-preserving flow. We have a relatively good understanding of these flows f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9ee960ea42e866c9a7c43e344ddaaf21
http://www.aimspress.com/article/doi/10.3934/mine.2021047?viewType=HTML
http://www.aimspress.com/article/doi/10.3934/mine.2021047?viewType=HTML
Autor:
Aya Ishizeki, Takeyuki Nagasawa
Publikováno v:
The Journal of Geometric Analysis. 31:5659-5686
The Mobius energy is one of the knot energies, and is named after its Mobius invariant property. It is known to have several different expressions. One is in terms of the cosine of conformal angle, and is called the cosine formula. Another is the dec
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::05734961328d192edf517161ed87cf55
https://doi.org/10.1007/s12220-020-00496-x
https://doi.org/10.1007/s12220-020-00496-x
Publikováno v:
Journal of Knot Theory and Its Ramifications. 31
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 the surrounding space. The starting point for this new discretizat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::eb9c6978bdd01741ccf9b063e5a09cda
https://doi.org/10.1142/s021821652250016x
https://doi.org/10.1142/s021821652250016x
Autor:
Aya Ishizeki, Takeyuki Nagasawa
Publikováno v:
Mathematische Zeitschrift.
O’Hara introduced several functionals as knot energies. One of them is the Mobius energy. We know its Mobius invariance from Doyle-Schramm’s cosine formula. It is also known that the Mobius energy was decomposed into three components keeping the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5745a9cc11635731cd3db80244411c1b
https://doi.org/10.1007/s00209-020-02601-w
https://doi.org/10.1007/s00209-020-02601-w
Autor:
Takeyuki Nagasawa, Kohei Nakamura
Publikováno v:
Adv. Differential Equations 24, no. 9/10 (2019), 581-608
Several inequalities for the isoperimetric ratio for plane curves are derived. In particular, we obtain interpolation inequalities between the deviation of curvature and the isoperimetric ratio. As applications, we study the large-time behavior of so
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::db18cf863168cffffc7a9f102b0d279b
https://projecteuclid.org/euclid.ade/1565661673
https://projecteuclid.org/euclid.ade/1565661673
Autor:
Takeyuki Nagasawa, Shoya Kawakami
Publikováno v:
Journal of Knot Theory and Its Ramifications. 29:2050017
O’Hara’s energies, introduced by Jun O’Hara, were proposed to answer the question what the canonical shape in a given knot type is, and were configured so that the less the energy value of a knot is, the “better” its shape is. The existence
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f123dad6d5d7eed8aa0ece83c5b1ab4a
https://doi.org/10.1142/s0218216520500170
https://doi.org/10.1142/s0218216520500170
Autor:
Takeyuki Nagasawa, Aya Ishizeki
Publikováno v:
Mathematische Annalen. 363:617-635
It was shown in a preceding paper that the Mobius energy can be decomposed into three parts and the Mobius invariance of each part was investigated. In this paper, we provide analytic application of our decomposition. Variational formulae of the Mobi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2698623b8014c9e38df2470096a2f09a
https://doi.org/10.1007/s00208-015-1175-2
https://doi.org/10.1007/s00208-015-1175-2
Autor:
Takeyuki Nagasawa
Publikováno v:
New Directions in Geometric and Applied Knot Theory ISBN: 9783110571493
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::83a917eaaa201dfd28739620e5016b1b
https://doi.org/10.1515/9783110571493-003
https://doi.org/10.1515/9783110571493-003
Autor:
Aya Ishizeki, Takeyuki Nagasawa
Publikováno v:
Calculus of Variations and Partial Differential Equations. 55
The Mobius energy is an example of a knot energy, so-called since it is invariant under Mobius transformations. It has been shown that it is defined on the fractional Sobolev space $$ H^{ \frac{3}{2} } \cap W^{1, \infty } $$ , where it can be decompo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2e0a83f6b47cbd8f232f448e371364d6
https://doi.org/10.1007/s00526-016-0993-8
https://doi.org/10.1007/s00526-016-0993-8