In this short note, we prove a convergence theorem for sequences of immersions from some closed surface into some standard Euclidean space with -bounded second fundamental form, which is suitable for the variational analysis of the famous Willmore functional, where . More precisely, under some assumptions which are automatically verified (up to subsequence and an appropriate Möbius transformation of ) by sequences of immersions from some closed surface into some standard Euclidean space arising from an appropriate stereographic projection of into of immersions from into and minimizing the -norm of the second fundamental form with , we show that the varifolds limit of the image of the measures induced by the sequence of immersions is also an immersion with some minimizing properties.
Cite this article
Cheikh Birahim Ndiaye, Reiner Schätzle, A Convergence Theorem for Immersions with -Bounded Second Fundamental Form. Rend. Sem. Mat. Univ. Padova 127 (2012), pp. 235–247DOI 10.4171/RSMUP/127-12