Compact Complete Minimal Immersions In
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چکیده
ANTONIO ALARC´ON ABSTRACT. In this paper we construct complete minimal surfaces with boundary in R 3 of arbitrary finite topology. For any arbitrary finite topological type we find a compact Riemann surface M, an open domain M ⊂ M with the fixed topological type, and a conformal complete minimal immersion X : M → R 3 which can be extended to a continuous map X : M → R 3 , such that X |∂M is an embedding and the Hausdorff dimension of X(∂M) is 1. We also prove that complete minimal surfaces with boundary are dense in the space of minimal surfaces with boundary in R 3 , endowed with the topology of the Hausdorff distance.
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. D G ] 3 0 A pr 2 00 8 COMPACT COMPLETE PROPER MINIMAL IMMERSIONS IN STRICTLY CONVEX BOUNDED REGULAR DOMAINS
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