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Classification of hyperbolic space-like constant mean curvature surfaces in Minkowski space

PERLI, ELIA ANDREA
2024/2025
MATEMATICA [08406]
2024
The thesis is aimed at the study of complete hyperbolic space-like constant mean curvature surfaces (CMCs) in Minkowski $3$-space. After introducing the necessary preliminary material on space-like surfaces in Minkowski space, harmonic maps, and holomorphic quadratic differentials, our work focuses on translating the geometric properties derived from the constant mean curvature hypothesis into analytic properties. In particular, we construct a map that associates a holomorphic quadratic differential on the Poincaré disk to each CMC cut. We then invert this correspondence, proving that this map is a bijection using the previously established properties. This reduces the problem to the study of a nonlinear PDE for the conformal factor of the induced metric. The last part of the thesis is therefore devoted to proving existence, by means of a sub- and supersolution method, and uniqueness, by means of a generalized maximum principle.
Lauree Magistrali
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.14239/34741