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- W4376869989 abstract "It has been shown in [17] that, for given |c|<1, the moduli space of constant mean curvature (CMC) c-immersions of a closed orientable surface of genus g≥2 into a hyperbolic 3-manifold can be parametrized by elements of the tangent bundle of the corresponding Teichmüller space. This is attained by showing the unique solvability of the Gauss-Codazzi equations governing (CMC) c-immersions. The corresponding unique solution is identified as the global minimum (and only critical point) of the Donaldson functional Dt (introduced in [11]) given in (1.11) with t=1−c2. When |c|≥1 (i.e. t≤0), so far nothing is known about the existence of analogous (CMC) c-immersions. Indeed, for t≤0 the functional Dt may no longer be bounded from below and evident non-existence situations do occur. Already the case |c|=1 (i.e. t=0) appears rather involved and actually (CMC) 1-immersions can be attained only as “limits” of (CMC) c-immersions for |c|⟶1− (see Theorem 2). To handle this situation, here we analyze the asymptotic behavior of minimizers of Dt as t⟶0+. We use an accurate asymptotic analysis (see [35]) to describe possible blow-up phenomena. In this way, we can relate the existence of (CMC) 1-immersions to the Kodaira map defined in (1.9). As a consequence, we obtain the first existence and uniqueness result about (CMC) 1-immersions of surfaces of genus g=2 into hyperbolic 3-manifolds." @default.
- W4376869989 created "2023-05-18" @default.
- W4376869989 creator A5021214570 @default.
- W4376869989 date "2023-07-01" @default.
- W4376869989 modified "2023-09-29" @default.
- W4376869989 title "Asymptotics for minimizers of a Donaldson functional and mean curvature 1-immersions of surfaces into hyperbolic 3-manifolds" @default.
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- W4376869989 doi "https://doi.org/10.1016/j.aim.2023.109090" @default.
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