• Corpus ID: 204734616

High energy harmonic maps and degeneration of minimal surfaces

  title={High energy harmonic maps and degeneration of minimal surfaces},
  author={Charles Ouyang},
  journal={arXiv: Differential Geometry},
  • Charles Ouyang
  • Published 15 October 2019
  • Mathematics
  • arXiv: Differential Geometry
Let $S$ be a closed surface of genus $g \geq 2$ and let $\rho$ be a maximal $\mathrm{PSL}(2, \mathbb{R}) \times \mathrm{PSL}(2, \mathbb{R})$ surface group representation. By a result of Schoen, there is a unique $\rho$-equivariant minimal surface $\widetilde{\Sigma}$ in $\mathbb{H}^{2} \times \mathbb{H}^{2}$. We study the induced metrics on these minimal surfaces and prove the limits are precisely mixed structures. In the second half of the paper, we provide a geometric interpretation: the… 

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