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

TL;DR

This paper proves angular energy quantization for solutions to 2D elliptic systems with antisymmetric potentials, leading to full energy quantization results for conformally invariant functionals and pseudo-holomorphic curves.

Contribution

It introduces a novel angular energy quantization result for elliptic systems with antisymmetric potentials, extending to critical points of conformally invariant functionals.

Findings

Angular energy quantization established for solutions to elliptic systems.

Full energy quantization derived for pseudo-holomorphic curves.

Uniform Lorentz-Wente estimates are key to the results.

Abstract

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.