15 citations · 28 across the 10 of their papers we have counts for
10 papers
The Classification of Rotationally symmetric hypersurfaces in the Heisenberg groups
Hung-Lin Chiu, Sin-Hua Lai, Hsiao-Fan Liu
In this paper, we show the fundamental theorems for rotationally symmetric hypersurfaces, and thus, together with the earlier results in [3] and [4], provide a complete classificat…
On Invariants of Constant -Mean Curvature Surfaces in the Heisenberg Group
Hung-Lin Chiu, Sin-Hua Lai, Hsiao-Fan Liu
One primary objective in submanifold geometry is to discover fascinating and significant classical examples of . In this paper which relies on the theory we established in [Ad…
Sturm-Liouville-type operators with frozen argument and Chebyshev polynomials
Tzong-Mo Tsai, Hsiao-Fan Liu, Sergey Buterin +2
The paper deals with Sturm-Liouville-type operators with frozen argument of the form where and is…
A characterization of constant -mean curvature surfaces in the Heisenberg group
Hung-Lin Chiu, Hsiao-Fan Liu
In Euclidean -space, it is well known that the Sine-Gordon equation was considered in the nineteenth century in the course of investigations of surfaces of constant Gaussian cur…
Geometric Algorithm of Schrödinger Flow on a Sphere
Hsiao-Fan Liu
We construct the solution to the periodic Cauchy problem of the Schrödinger flow on the sphere. Such construction of solutions is formulated explicitly and therefore a geometric al…
A q-generalization of the Toda equations for the q-Laguerre/Hermite orthogonal polynomials
Chuan-Tsung Chan, Hsiao-Fan Liu
Based on the motivation of generalizing the correspondence between the Lax equation for the Toda lattice and the deformation theory of the orthogonal polynomials, we derive a q-def…
Star Mean Curvature Flow on 3 manifolds and its Bäcklund Transformations
Hsiao-Fan Liu
The Hodge star mean curvature flow on a 3-dimensional Riemannian or pseudo-Riemannian manifold is a natural nonlinear dispersive curve flow in geometric analysis. A curve flow is i…
Graphic Enumerations and Discrete Painlevé Equations via Random Matrix Models
Chuan-Tsung Chan, Hsiao-Fan Liu
We revisit the enumeration problems of random discrete surfaces (RDS) based on solutions of the discrete equations derived from the matrix models. For RDS made of squares, the recu…
-soliton formula and blowup result of the Wadati-Konno-Ichikawa equation
Hsiao-Fan Liu, Yusuke Shimabukuro
We formulate the soliton solution of the Wadati-Konno-Ichikawa equation that is determined by purely algebraic equations. Derivation is based on the matrix Riemann-Hilbert prob…
Anatomy of a q-generalization of the Laguerre/Hermite Orthogonal Polynomials
Chuan-Tsung Chan, Hsiao-Fan Liu
We study a q-generalization of the classical Laguerre/Hermite orthogonal polynomials. Explicit results include: the recursive coefficients, matrix elements of generators for the He…