Angular Energy Quantization for Linear Elliptic Systems with Antisymmetric Potentials and Applications

Details Angular Energy Quantization for Linear Elliptic Systems with Antisymmetric Potentials and Applications Angular Energy Quantization for Linear Elliptic Systems with Antisymmetric Potentials and Applications

2011-09-16

arxiv.org/abs/1109.3599v1

Mathematics

Analysis of PDEs

38 pages, 2 figures

Scientific paper

In the present work we establish a quantization result for the angular part of the energy of solu- tions to elliptic linear systems of Schr\"odinger type with antisymmetric potentials in two dimension. This quantization is a consequence of uniform Lorentz-Wente type estimates in degenerating annuli. We derive from this angular quantization the full energy quantization for general critical points to functionals which are conformally invariant or also for pseudo-holomorphic curves on degenerating Riemann surfaces.

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