Browsing by Author "Ouyang, Charles"

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    Degeneration of minimal surfaces in the bidisc
    (2020-04-22) Ouyang, Charles; Wolf, Michael
    This thesis studies the degeneration of a particular class of minimal surfaces in the bidisc, describing both the limiting metric structure and geometry. Minimal surfaces inside symmetric spaces have been shown to be directly related to surface group representations into higher rank Lie groups by recent work of Labourie. Let S be a closed surface of genus g ≥ 2 and let ρ be a maximal PSL(2, R) × PSL(2, R) surface group representation. By a result of Schoen, there is a unique ρ-equivariant minimal surface Σ in H2 × H2. We study the induced metrics on these minimal surfaces and prove the limits are precisely mixed structures. In the second half of the thesis, we provide a geometric interpretation: the minimal surfaces Σ degenerate to the core of a product of two R-trees. As a consequence, we obtain a geometric compactification of the space of maximal representations of π1(S) into PSL(2, R) × PSL(2, R).