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- W2952977503 abstract "For any open orientable surface $M$ and convex domain $Omegasubset mathbb{C}^3,$ there exists a Riemann surface $N$ homeomorphic to $M$ and a complete proper null curve $F:NtoOmega.$ This result follows from a general existence theorem with many applications. Among them, the followings: For any convex domain $Omega$ in $mathbb{C}^2$ there exist a Riemann surface $N$ homeomorphic to $M$ and a complete proper holomorphic immersion $F:NtoOmega.$ Furthermore, if $D subset mathbb{R}^2$ is a convex domain and $Omega$ is the solid right cylinder ${x in mathbb{C}^2 | {Re}(x) in D},$ then $F$ can be chosen so that ${rm Re}(F):Nto D$ is proper. There exists a Riemann surface $N$ homeomorphic to $M$ and a complete bounded holomorphic null immersion $F:N to {rm SL}(2,mathbb{C}).$ There exists a complete bounded CMC-1 immersion $X:M to mathbb{H}^3.$ For any convex domain $Omega subset mathbb{R}^3$ there exists a complete proper minimal immersion $(X_j)_{j=1,2,3}:M to Omega$ with vanishing flux. Furthermore, if $D subset mathbb{R}^2$ is a convex domain and $Omega={(x_j)_{j=1,2,3} in mathbb{R}^3 | (x_1,x_2) in D},$ then $X$ can be chosen so that $(X_1,X_2):Mto D$ is proper. Any of the above surfaces can be chosen with hyperbolic conformal structure." @default.
- W2952977503 created "2019-06-27" @default.
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- W2952977503 date "2009-12-15" @default.
- W2952977503 modified "2023-09-26" @default.
- W2952977503 title "Null Curves in $mathbb{C}^3$ and Calabi-Yau Conjectures" @default.
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