arXiv subjects

Chen-Kuan Lee

Publications and source records attributed to Chen-Kuan Lee.

3 recordsLinked to original sources

arXiv2025

Uniqueness in the Plateau problem for calibrated currents

We show that every compactly supported smoothly calibrated integral current with connected $C^{3,α}$ boundary is the unique solution to the oriented Plateau problem for its boundary data. The same holds true for compactly supported $``$continuously calibrated$"$ integral flat chains. This is proved as a consequence of the boundary regularity theory for area-minimizing currents and a unique continuation argument in the spirit of Frank Morgan. In codimension one, the argument yields a sufficient condition for uniqueness in the oriented Plateau problem expressed in terms of the regularity of the calibrating form.

math.DG↗

arXiv2025

Perturbations of a minimal surface with triple junctions in $\mathbb{R}^2 \times \mathbb{S}^1$

We construct stationary perturbations of a specific minimal surface with a circle of triple junctions in $\mathbb{R}^2 \times \mathbb{S}^1$, that satisfy given boundary data.

math.DG↗

arXiv2023

Self-expanders to the mean curvature flow based on the generalized Lawson-Osserman cone

We derive the equation of self-similar solutions to mean curvature flow based on the generalized Lawson-Osserman cone and prove the existence of self-expanders by modifying the theory of equilibria in the autonomous system. In particular, those self-expanders are unique if a local assumption is given.

math.DG↗