Author

Parker Evans

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Preprint Oct 2026

Polynomial Maximal Surfaces in H^{2,2} and Spherical Polygons

We study the moduli space of complete maximal surfaces in pseudo-hyperbolic space $\mathbf{H}^{2,2}$ with polygonal asymptotic boundary a lightlike $(n+4)$-gon in the Einstein universe $\mathbf{Ein}^{1,2}$, up to the action of $\mathsf{SO}_0(2,3)$. Importantly, this space $M_{n+4}(\mathbf{H}^{2,2})$ is disconnected for...

Parker Evans, A. Moriani · 0 citations

Preprint Sep 2026

On Line-Hyperplane Structures for Hitchin Representations

Let $n \geq 4$ and $\rho: \pi_1S \rightarrow PSL(n,\mathbb{R})$ be a Hitchin representation. We study the topology of a cocompact domain of discontinuity $\Omega_{\rho}$ in the flag manifold $\mathcal{F}_{1,n-1}$ of line-hyperplane pairs in $\mathbb{R}^n$ defined by Guichard-Wienhard. In particular, we lift $\Omega$ to...

Parker Evans, Andrea Tamburelli · 0 citations