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Award ID contains: 2005551

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  1. ; (, Bulletin of the London Mathematical Society)
    Abstract We show that recent work of Song implies that torsion‐free hyperbolic groups with Gromov boundary arerealized as fundamental groups of closed 3‐manifolds of constant negative curvature if and only if the solution to an associated spherical Plateau problem for group homology is isometric to such a 3‐manifold, and suggest some related questions. 
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  2. (, Advances in Mathematics)
    Free, publicly-accessible full text available February 1, 2026
  3. ; (, American journal of mathematics)
    We study the asymptotic geometry of a family of conformally planar minimal surfaces with polynomial growth in the Sp(4,R)-symmetric space. We describe a homeomorphism between the “Hitchin component” of wild Sp(4,R)- Higgs bundles over CP1 with a single pole at infinity and a component of maximal surfaces with light-like polygonal boundary in H2,2. Moreover, we identify those surfaces with convex embeddings into the Grassmannian of symplectic planes of R4. We show, in addition, that our planar maximal surfaces are the local limits of equivariant maximal surfaces in H2,2 associated to Sp(4,R)-Hitchin representations along rays of holomorphic quartic differentials. 
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    Free, publicly-accessible full text available January 1, 2026
  4. (, Advances in Mathematics)
    Full Text Available 
  5. ; ; (, Annales Scientifiques de lEcole Normale Supérieure)
    We define and prove the existence of unique solutions of an asymptotic Plateau problem for spacelike maximal surfaces in the pseudo-hyperbolic space of signature (2, n): the boundary data is given by loops on the boundary at infinity of the pseudo-hyperbolic space which are limits of positive curves. We also discuss a compact Plateau problem. The required compactness arguments rely on an analysis of the pseudo-holomorphic curves defined by the Gauß lifts of the maximal surfaces. 
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    Accepted Manuscript Full Text Available
  6. ; ; ; (, Geometry & Topology)
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