Author

Qiongling Li

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Preprint Sep 2026

Harmonic Maps from Punctured Riemann Surfaces to the Hyperbolic Plane with Prescribed Scherk Asymptotics

Let $X$ be a genus $g\geq 0$ compact Riemann surface that admits an antiholomorphic involution $\iota$ with non empty fixed-point set, and let $D = \{p_1,\dots,p_k\}\subset \text{Fix}(\iota)$. At each puncture, we prescribe a Scherk map associated to a given real polynomial quadratic differential with even degree and n...

Qiongling Li, Jin-Song Liu, Yi-Hui Xu · 0 citations

Preprint Sep 2026

Non-maximal quasi-isometric $\mathrm{PU}_{2,n+1}$-representations via alternating surfaces in complex pseudo-hyperbolic spaces

For every admissible non-maximal Toledo invariant $t$, we construct a locus of irreducible representations of a closed genus-$g$ surface group into $\mathrm{PU}_{2,n+1}$ with Toledo invariant $t$ whose orbit maps are quasi-isometric embeddings. These loci have real codimension $10(g-1)$ or $10(g-1)+2(n-1)$ in the chara...

Qiongling Li, Jun-Ming Zhang · 0 citations