arXiv subjects

Huy The Nguyen

Publications and source records attributed to Huy The Nguyen.

21 records · Page 2Linked to original sources

arXiv2014

Quantitative rigidity results for conformal immersions

In this paper we prove several quantitative rigidity results for conformal immersions of surfaces in $\mathbb{R}^n$ with bounded total curvature. We show that (branched) conformal immersions which are close in energy to either a round sphere, a conformal Clifford torus, an inverted catenoid, an inverted Enneper's minimal surface or an inverted Chen's minimal graph must be close to these surfaces in the $W^{2,2}$-norm. Moreover, we apply these results to prove a corresponding rigidity result for complete, connected and non-compact surfaces.

math.DG↗

arXiv2014

A Gap Theorem for Willmore Tori and an application to the Willmore Flow

In 1965 Willmore conjectured that the integral of the square of the mean curvature of a torus immersed in $R^3$ is at least $2π^2$ and attains this minimal value if and only if the torus is a Möbius transform of the Clifford torus. This was recently proved by Marques and Neves. In this paper, we show for tori there is a gap to the next critical point of the Willmore energy and we discuss an application to the Willmore flow. We also prove an energy gap from the Clifford torus to surfaces of higher genus.

math.DG↗

arXiv2011

Branched Willmore Spheres

In this paper we classify branched Willmore spheres with at most three branch points (including multiplicity), showing that they may be obtained from complete minimal surfaces in $\R ^ 3$ with ends of multiplicity at most three. This extends the classification result of Bryant. We then show that this may be applied to the analysis of singularities of the Willmore flow of non-Willmore spheres with Willmore energy $ \mc {W} (f) \leq 16π$.

math.DG↗