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Angular energy
quantization for linear elliptic systems with antisymmetric
potentials and applications
Paul Laurain and Tristan Rivière |
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Vol. 7 (2014), No. 1, 1–41
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Abstract |
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We establish a quantization result for the angular part of the energy of solutions to elliptic linear systems of Schrödinger type with antisymmetric potentials in two dimensions. This quantization is a consequence of uniform Lorentz–Wente type estimates in degenerating annuli. Moreover this result is optimal in the sense that we exhibit a sequence of functions satisfying our hypothesis whose radial part of the energy is not quantized. We derive from this angular quantization the full energy quantization for general critical points to functionals which are conformally invariant or also for pseudoholomorphic curves on degenerating Riemann surfaces. |
Keywords
analysis of PDEs, differential geometry
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Mathematical Subject Classification 2010
Primary: 35J20, 35J60, 53C42, 58E20, 35J47
Secondary: 49Q05, 53C21, 32Q65
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Milestones
Received: 1 December 2011
Revised: 7 February 2013
Accepted: 3 April 2013
Published: 7 May 2014
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Authors |
| Paul Laurain | |
| Department of Mathematics IMJ-Université Paris 7 75013 Paris France |
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| http://www.math.jussieu.fr/~laurainp/ | |
| Tristan Rivière | |
| Department of Mathematics ETH Zentrum CH-8093 Zürich Switzerland |
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| http://www.math.ethz.ch/~riviere/ | |
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