arXiv subjects

Yong Chan Kim

Publications and source records attributed to Yong Chan Kim.

6 recordsLinked to original sources

arXiv2026

Raman Circular Dichroism Reveals Higher-Order Quantum Geometry of Magnons

We develop a gauge-invariant framework that relates two-magnon Raman circular dichroism (RCD) to higher-order magnon quantum geometry. In the magnon band basis, the Raman operator decomposes into interband Berry connections, their covariant derivatives, and products of successive connections, generating higher-order, multi-state geometric tensors beyond the conventional single-band quantum metric and Berry curvature. Applying this framework to a field-polarized Kitaev magnet, we show that higher-order geometric tensors govern the dichroic response. Our results establish RCD as a spectroscopic probe of generalized magnon quantum geometry.

cond-mat.str-el↗

arXiv2012

Univalence criteria and analogs of the John constant

Let $p(z)=zf'(z)/f(z)$ for a function $f(z)$ analytic on the unit disk $|z|<1$ in the complex plane and normalized by $f(0)=0, f'(0)=1.$ We will provide lower and upper bounds for the best constants $δ_0$ and $δ_1$ such that the conditions $e^{-δ_0/2}<|p(z)|<e^{δ_0/2}$ and $|p(w)/p(z)|<e^{δ_1}$ for $|z|,|w|<1$ respectively imply univalence of $f$ on the unit disk.

math.CV↗

arXiv2011

On univalence of the power deformation $z(f(z)/z)^c$

In this note, we mainly concern the set $U_f$ of $c\in\mathbb{C}$ such that the power deformation $z(f(z)/z)^c$ is univalent in the unit disk $|z|<1$ for a given analytic univalent function $f(z)=z+a_2z^2+\cdots$ in the unit disk. We will show that $U_f$ is a compact, polynomially convex subset of the complex plane $\C$ unless $f$ is the identity function. In particular, the interior of $U_f$ is simply connected. This fact enables us to apply various versions of the $λ$-lemma for the holomorphic family $z(f(z)/z)^c$ of injections parametrized over the interior of $U_f.$ We also give necessary or sufficient conditions for $U_f$ to contain $0$ or $1$ as an interior point.

math.CV↗

arXiv2011

On power deformations of univalent functions

For an analytic function $f(z)$ on the unit disk $|z|<1$ with $f(0)=f'(0)-1=0$ and $f(z)\ne0, 0<|z|<1,$ we consider the power deformation $f_c(z)=z(f(z)/z)^c$ for a complex number $c.$ We determine those values $c$ for which the operator $f\mapsto f_c$ maps a specified class of univalent functions into the class of univalent functions. A little surprisingly, we will see that the set is described by the variability region of the quantity $zf'(z)/f(z),~|z|<1,$ for the class in most cases which we consider in the present paper. As an unexpected by-product, we show boundedness of strongly spirallike functions.

math.CV↗

arXiv2010

Correspondence between spirallike functions and starlike functions

Let $λ$ be a real number with $-π/2<λ<π/2.$ In order to study $λ$-spirallike functions, it is natural to measure the angle according to $λ$-spirals. Thus we are led to the notion of $λ$-argument. This fits well the classical correspondence between $λ$-spirallike functions and starlike functions. Using this idea, we extend deep results of Pommerenke and Sheil-Small on starlike functions to spirallike functions. As an application, we solved a problem given by Hansen in 1971.

math.CV↗

arXiv2010

Hardy spaces and unbounded quasidisks

We study the maximal number $0\le h\le+\infty$ for a given plane domain $Ω$ such that $f\in H^p$ whenever $p<h$ and $f$ is analytic in the unit disk with values in $Ω.$ One of our main contributions is an estimate of $h$ for unbounded $K$-quasidisks.

math.CV↗