Yoshihisa Miyanishi

activity

20132024

most citedWeyl's law for the eigenvalues of the Neumann--Poincaré operators in three dimensions: Willmore energy and surface geometry

17 citations · 70 across the 20 of their papers we have counts for

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Showing 2018Show all

4 papers · 1 filter

math.FA2018★ 1 cited

Eigenvalues of the Neumann-Poincare operator in dimension 3: Weyl's law and geometry

Yoshihisa Miyanishi, Grigori Rozenblum

We consider the asymptotic properties of the eigenvalues of the Neumann-Poincare (NP) operator in three dimensions. The region $Ω \subset R^{3}$ is bounded by a compact surfa…

math.SP2018★ 11 cited

Spectral structure of the Neumann--Poincaré operator on tori

Kazunori Ando, Yong-Gwan Ji, Hyeonbae Kang +2

We address the question whether there is a three-dimensional bounded domain such that the Neumann--Poincaré operator defined on its boundary has infinitely many negative eigenvalue…

math.SP2018★ 17 cited

Weyl's law for the eigenvalues of the Neumann--Poincaré operators in three dimensions: Willmore energy and surface geometry

Yoshihisa Miyanishi

We deduce eigenvalue asymptotics of the Neumann--Poincaré operators in three dimensions. The region $Ω$ is $C^{2, α}$ ( $α > 0$ ) bounded in $R^{3}$ and the Neumann--Poincaré o…

math.SP2018★ 1 cited

The first Hadamard variation of Neumann-Poincaré eigenvalues on the sphere

Kazunori Ando, Hyeonbae Kang, Yoshihisa Miyanishi +1

The Neumann-Poincaré operator on the sphere has $\frac{1}{2 ( 2 k + 1 )}$ , $k = 0, 1, 2, \dots$ , as its eigenvalues and the corresponding multiplicity is $2 k + 1$ . We consider the bifurcation…