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- W2963157130 abstract "We study a recent general criterion for the injectivity of the conformal immersion of a Riemannian manifold into higher dimensional Euclidean space, and show how it gives rise to important conditions for Weierstrass–Enneper lifts defined in the unit disk $$mathbb{D}$$ endowed with a conformal metric. Among the corollaries, we obtain a Becker type condition and a sharp condition depending on the Gaussian curvature and the diameter for an immersed geodesically convex minimal disk in $$mathbb{R}^3$$ to be embedded. Extremal configurations for the criteria are also determined, and can only occur on a catenoid. For non-extremal configurations, we establish fibrations of space by circles in domain and range that give a geometric analogue of the Ahlfors–Weill extension." @default.
- W2963157130 created "2019-07-30" @default.
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- W2963157130 date "2017-04-01" @default.
- W2963157130 modified "2023-10-18" @default.
- W2963157130 title "Injectivity of minimal immersions and homeomorphic extensions to space" @default.
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- W2963157130 doi "https://doi.org/10.1007/s11856-017-1505-z" @default.
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