科研之友
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摘要
For mappings from S (2m) to a compact manifold , we identify energies of order m that are invariant under conformal transformations of S (2m) , which we call Paneitz energies. We study the behavior of minimizing sequences for such Paneitz energies within a given free homotopy class . Either a subsequence converges in W (m,2) to a minimizer of the Paneitz energy, or we have only weak convergence, and Paneitz energy concentrates at finitely many points of S (2m) . Conformal rescalings reveal bubbles, i.e. Paneitz-polyharmonic spheres, that are responsible for both energy loss and topology changes in the limit of the minimizing sequence.
- 出版日期2013-7
