# High energy harmonic maps and degeneration of minimal surfaces

@article{Ouyang2019HighEH, title={High energy harmonic maps and degeneration of minimal surfaces}, author={Charles Ouyang}, journal={arXiv: Differential Geometry}, year={2019} }

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…

## 6 Citations

Length spectrum compactification of the $\mathrm{SO}_{0}(2,3)$-Hitchin component

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We show that, in the character variety of surface group representations into the Lie group PSL(2,R) × PSL(2,R), the compactification of the maximal component introduced by the second author is a…

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In this short note we describe an interesting new phenomenon about the Sp(4,R)-character variety. Precisely, we show that the Hitchin component and all Gothen components share the same boundary in…

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We find a compactification of the $\mathrm{SL}(3,\mathbb{R})$-Hitchin component by studying the degeneration of the Blaschke metrics on the associated equivariant affine spheres. In the process, we…

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