2014/08/09 by Lamm, Tobias, Schätzle, Reiner M.
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1408.2089
In this paper we show a quantitative rigidity result for the minimizer of the Willmore functional among all projective planes in ℝn with n≥ 4. We also construct an explicit counterexample to a corresponding rigidity result in codimension one, by showing that an Enneper surface might split-off during a blow-up process. For conformal immersions of spheres with large enough Willmore energies, we construct explicit counterexamples to a quantitative rigidity result and this complements the recently obtained rigidity results in [LaNg13].