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

2011/09/16 by Paul Laurain, Laurain, Paul, Tristan Rivière +1 · 4 citations
Mathematics · #Geometric Analysis and Curvature Flows #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.1109.3599

Abstract

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

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