4 papers
A Discrete-to-Continuum Variational Theory for Area-Preserving Surface Parameterization
Shu-Yung Liu, Kento Sakai, Mei-Heng Yueh
We establish a discrete-to-continuum variational theory for area-preserving parameterization of surfaces based on the stretch energy. For orientation-preserving diffeomorphisms bet…
Electric Teichmüller spaces and -multicurve graphs
Kento Sakai
Masur and Minsky showed that the curve graph is quasi-isometric to the Teichmüller space electrified along its thin part, and hence the Teichmüller space is weakly relatively hyper…
Large-scale geometry of graphs interpolating between curve graphs and pants graphs
Erika Kuno, Rin Kuramochi, Kento Sakai
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…
Uniform degeneration of hyperbolic surfaces with boundary along harmonic map rays
Kento Sakai
We study the degeneration of hyperbolic surfaces along a ray given by the harmonic map parametrization of Teichmüller space. The direction of the ray is determined by a holomorphic…