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Conformal energy in four dimension |
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| Authors: | X Xu PC Yang |
| Institution: | (1) Department fdof Mathematics, National University of Singapore, 2 Science Drive 2, 117543 Singapore (e-mail: matxuxw@@nus.edu.sg) , SG;(2) Department of Mathematics, Princeton University, Princeton, NJ 08540, USA (e-mail: yang@@math.princeton.edu) , US |
| Abstract: | The conformal energy for 4-manifolds using the Paneitz operator is introduced in this article. The conformal invariance of the energy functional allows us to find a sharp lower bound in terms of the conformal volume. We also demonstrate certain obstruction to existence of minimal immersions to spheres using the fourth order curvature invariance associated to the operator. Received: 17 April 1999 / Revised version: 23 March 2002 / Published online: 5 September 2002 |
| Keywords: | Mathematics Subject Classification (1991): 53c 58G |
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