Performance information

• A Möbius invariant discretization of O’Hara’s Möbius energy
  Simon Blatt; Aya Ishizeki; Takeyuki Nagasawa
  Journal of Knot Theory and Its Ramifications, Volume：31, Number：03, Mar. 2022, [Reviewed]
  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 discretization is the cosine formula of Doyle and Schramm. We then show [Formula: see text]-convergence of our discretized energies to the Möbius energy.
  World Scientific Pub Co Pte Ltd, Scientific journal
  DOI：https://doi.org/10.1142/s021821652250016x
  DOI ID：10.1142/s021821652250016x, ISSN：0218-2165, eISSN：1793-6527
• Decomposition of generalized O’Hara’s energies
  Aya Ishizeki; Takeyuki Nagasawa
  Mathematische Zeitschrift, Oct. 2020, [Reviewed]
  Springer Science and Business Media LLC, Scientific journal
  DOI：https://doi.org/10.1007/s00209-020-02601-w
  DOI ID：10.1007/s00209-020-02601-w, ISSN：0025-5874, eISSN：1432-1823
• Upper and Lower Bounds and Modulus of Continuity of Decomposed Möbius Energies
  Aya Ishizeki; Takeyuki Nagasawa
  The Journal of Geometric Analysis, Volume：31, Number：6, First page：5659, Last page：5686, Aug. 2020, [Reviewed]
  Springer Science and Business Media LLC, Scientific journal
  DOI：https://doi.org/10.1007/s12220-020-00496-x
  DOI ID：10.1007/s12220-020-00496-x, ISSN：1050-6926, eISSN：1559-002X
• The $$ L^2 $$ L 2 -gradient of decomposed Möbius energies
  Aya Ishizeki; Takeyuki Nagasawa
  Calculus of Variations and Partial Differential Equations, Volume：55, Number：3, May 2016, [Reviewed]
  Springer Science and Business Media LLC, Scientific journal
  DOI：https://doi.org/10.1007/s00526-016-0993-8
  DOI ID：10.1007/s00526-016-0993-8, ISSN：0944-2669, eISSN：1432-0835
• The invariance of decomposed Möbius energies under inversions with center on curves
  Aya Ishizeki; Takeyuki Nagasawa
  Journal of Knot Theory and Its Ramifications, Volume：25, Number：02, First page：1650009, Last page：1650009, Feb. 2016, [Reviewed]
  It is well known that one of O’Hara’s knot energies is called the Möbius energy because of its invariance under Möbius transformations. We showed in a previous paper that the Möbius energy can be decomposed into three parts that retain invariance but we left open the question of invariance regarding inversions with respect to spheres centered on a knot. Here, we answer this question under the assumption that the knots have extra regularity. The result holds not only for knots but also for closed curves in [Formula: see text].
  World Scientific Pub Co Pte Lt, Scientific journal
  DOI：https://doi.org/10.1142/s0218216516500097
  DOI ID：10.1142/s0218216516500097, ISSN：0218-2165, eISSN：1793-6527
• A decomposition theorem of the Möbius energy II: variational formulae and estimates　　　　　　　　　　　　　　　
  Aya Ishizeki
  Math. Ann. 363 (1-2), 617-635, 2015, [Reviewed]
  Scientific journal
  ORCID：210563537
• A decomposition theorem of the Möbius energy I: Decomposition and Möbius invariance　　　　　　　　　　　　　　　
  Aya Ishizeki; Takeyuki Nagasawa
  Kodai Mathematical Journal, Volume：37, Number：3, Oct. 2014, [Reviewed]
  Tokyo Institute of Technology, Department of Mathematics, Scientific journal
  DOI：https://doi.org/10.2996/kmj/1414674619
  DOI ID：10.2996/kmj/1414674619, ISSN：0386-5991