arXiv subjects

Kento Sakai

Publications and source records attributed to Kento Sakai.

6 recordsLinked to original sources

arXiv2026

Area-Preserving Parameterization: Variational Principle, Gradient Flow, and Discrete Approximation

Area-preserving parameterizations are used in applications where relative surface areas must be preserved. We study this problem through the stretch energy. For orientation-preserving diffeomorphisms between compact Riemannian 2-manifolds of equal total area, we show that the stretch energy is characterized by the variance of the area ratio and that its critical points are area-preserving. This variational characterization leads naturally to an $L^2$-gradient flow, which we call the authalic flow. We then develop its simplicial counterpart based on the discrete stretch energy and obtain computational methods for open and closed surfaces of several topological types. To connect the discrete formulation with the smooth theory, we prove the first-order consistency of the stretch energy with respect to mesh refinement and establish a first-order $L^2$ area-distortion bound for discrete global minimizers under the stated geometric approximation assumptions. Numerical experiments on benchmark meshes produce fold-free maps in all reported tests and show competitive area preservation compared with existing methods.

math.NA↗

arXiv2026

Electric Teichm\"uller spaces and $k$-multicurve graphs

Masur and Minsky showed that the curve graph is quasi-isometric to the Teichm\"uller space electrified along its thin part, and hence the Teichm\"uller space is weakly relatively hyperbolic with respect to the thin part. In this paper, we extend this result to the $k$-multicurve graph by electrifying the Teichm\"uller space along the thin part where the extremal length of $k$ curves is sufficiently small. A key ingredient is a bound on the $k$-multicurve graph distance in terms of the intersection number, which is obtained by adapting the upper bound for the pants graph due to Lackenby and Yazdi.

math.GT↗

arXiv2026

Large-scale geometry of graphs interpolating between curve graphs and pants graphs

We study two types of graphs interpolating between the curve graph and the pants graph from the viewpoint of large-scale geometry. One was introduced by Erlandsson and Fanoni, and the other by Mahan Mj. These graphs were developed independently in different contexts. In this paper, we provide explicit formulae for computing their quasi-flat ranks. These formulae depend on the genus and the number of boundary components of the underlying surface, as well as the interpolation parameter. We also classify geometries of the interpolating graphs into the hyperbolic, relatively hyperbolic, and thick cases. Our approach relies on the theory of twist-free graphs of multicurves, which is developed by Vokes and Russel.

math.GT↗

arXiv2024

Uniform degeneration of hyperbolic surfaces with boundary along harmonic map rays

We study the degeneration of hyperbolic surfaces along a ray given by the harmonic map parametrization of Teichm\"uller space. The direction of the ray is determined by a holomorphic quadratic differential on a punctured Riemann surface, which has poles of order $\geq 2$ at each puncture. We show that the rescaled distance functions of the universal covers of hyperbolic surfaces uniformly converge, on a certain non-compact region containing a fundamental domain, to the intersection number with the vertical measured foliation given by the holomorphic quadratic differential determining the direction of the ray. This implies that hyperbolic surfaces along the ray converge to the dual $\mathbb{R}$-tree of the vertical measured foliation in the sense of Gromov-Hausdorff. As an application, we determine the limit of the hyperbolic surfaces in the Thurston boundary.

math.GT↗

arXiv2024

X-ray Iron absorption line in Swift J1858.6-0814

We present the spectral analysis of bright steady states in an outburst of the transient neutron star low-mass X-ray binary (NS-LMXB) Swift J1858.6-0814 observed with NICER. We detected an ionized iron K absorption line (H-like Fe) at 6.97keV in the spectrum. We estimated the photoionization parameter using the ratio of the equivalent widths (EWs) of the FeXXVI (H-like) (17+\-5eV) and FeXXV (He-like) (<3eV) and discuss the origin of the iron absorption line. The irradiated gas producing the absorption line would locate within (3-6)*1E9cm from the X-ray source. We suggest that the observed H-like Fe absorption line originates from the highly-ionized gas in the inner accretion disk in Swift J1858.6-0814.

astro-ph.HE↗

arXiv2022

The harmonic maps compactification of Teichmüller spaces for punctured Riemann surfaces

Wolf gave a homeomorphism from the Teichmüller space to the space of quadratic differentials on a closed Riemann surface by using harmonic maps. Moreover, using harmonic maps rays, he gave a compactification of the Teichmüller space and show that it coincides with the Thurston compactification. In this paper, we extend the harmonic maps compactification to the Teichmüller spaces of punctured Riemann surfaces, and show that it still coincides with the Thurston compactification.

math.GT↗