A Convergence Theorem for Immersions with L-2-Bounded Second Fundamental Form

作者：Ndiaye Cheikh Birahim^*; Schaetzle Reiner

来源：Rendiconti del Seminario Matematico della Universita di Padova, 2012, 127: 235-247.

DOI：10.4171/RSMUP/127-12

In this short note, we prove a convergence theorem for sequences of immersions from some closed surface Sigma into some standard Euclidean space R-n with L-2-bounded second fundamental form, which is suitable for the variational analysis of the famous Willmore functional, where n %26gt;= 3. More precisely, under some assumptions which are automatically verified (up to subsequence and an appropriate Mobius transformation of R-n) by sequences of immersions from some closed surface Sigma into some standard Euclidean space R-n arising from an appropriate stereographic projection of S-n into R-n of immersions from Sigma into S-n and minimizing the L-2-norm of the second fundamental form with n %26gt;= 3, 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.

• 出版日期2012