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Katsuyuki Ishii

Publications and source records attributed to Katsuyuki Ishii.

4 recordsLinked to original sources
arXiv2024

A thresholding algorithm to Willmore-type flows via fourth order linear parabolic equation

We propose a thresholding algorithm to Willmore-type flows in $\mathbb{R}^N$. This algorithm is constructed based on the asymptotic expansion of the solution to the initial value problem for a fourth order linear parabolic partial differential equation whose initial data is the indicator function on the compact set $Ω_0$. The main results of this paper demonstrate that the boundary $\partialΩ(t)$ of the new set $Ω(t)$, generated by our algorithm, is included in $O(t)$-neighborhood of $\partialΩ_0$ for small $t>0$ and that the normal velocity from $ \partialΩ_0 $ to $ \partialΩ(t) $ is nearly equal to the $L^2$-gradient of Willmore-type energy for small $ t>0 $. Finally, numerical examples of planar curves governed by the Willmore flow are provided by using our thresholding algorithm.

math.AP↗
arXiv2014

Constrained WZWN Models on G/{S x U(1)^n} and Exchange Algebra of G-Primaries

Consistently constrained WZWN models on G/{S x U(1)^n} is given by constraining currents of the WZWN models with G. Poisson brackets are set up on the light-like plane. Using them we show the Virasoro algebra for the energy-momentum tensor of constrained WZWN models. We find a G-primary which satisfies a classical exchange algebra in an arbitrary representation of G. The G-primary and the constrained currents are also shown to obey the conformal transformation with respect to the energy-momentum tensor. It is checked that conformal weight of the constrained currents is 0. This is necessary for the consistency for our formulation of constrained WZWN models.

hep-th↗
arXiv2014

Consistently Constrained SL(N) WZWN Models and Classical Exchange Algebra

Currents of the SL(N) WZWN model are constrained so that the remaining symmetry is a symmetry of constrained currents as well. Such consistency enables us to study the Poisson structure of constrained SL(N) WZWN models properly. We establish the Poisson brackets which satisfy the Jacobi identities owing to the classical Yang-Baxter equation. The Virasoro algebra is shown by using them. An SL(N) conformal primary is constructed. It satisfies a quadratic algebra, which might become an exchange algebra by its quantum deformation.

hep-th↗