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A FAMILY OF TRIPLY PERIODIC COSTA SURFACES
 PACIFIC JOURNAL OF MATHEMATICS
, 2003
"... We derive global Weierstrass representations for complete minimal surfaces obtained by substituting the ends of the Costa surface by symmetry curves. ..."
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We derive global Weierstrass representations for complete minimal surfaces obtained by substituting the ends of the Costa surface by symmetry curves.
A characterisation of the HoffmanWohlgemuth surfaces in terms of their symmetries
 J. Differential Geom
"... For an embedded singly periodic minimal surface ˜ M with genus ≥ 4 and annular ends, some weak symmetry hypotheses imply its congruence with one of the HoffmanWohlgemuth examples. We give a very geometrical proof of this fact, along which they come out many valuable clues for the understanding of ..."
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For an embedded singly periodic minimal surface ˜ M with genus ≥ 4 and annular ends, some weak symmetry hypotheses imply its congruence with one of the HoffmanWohlgemuth examples. We give a very geometrical proof of this fact, along which they come out many valuable clues for the understanding of these surfaces. 1.
A note on the uniqueness of the periodic CallahanHoffmanMeeks surfaces in terms of their symmetries
, 1999
"... We give a new characterization of the periodic CallahanHoffmanMeeks surfaces in terms of their symmetries. ..."
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We give a new characterization of the periodic CallahanHoffmanMeeks surfaces in terms of their symmetries.
A Note on the Uniqueness of the Periodic Callahan^Hoffman^Meeks Surfaces in Terms of their Symmetries
, 2000
"... Abstract. We give a new characterization of the periodic Callahan^Hoffman^Meeks surfaces in terms of their symmetries. Mathematics Subject Classi¢cations (2000). Primary 53A10; Secondary 53C42. Key words. Periodic minimal surfaces, immersions, di¡erential geometry. ..."
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Abstract. We give a new characterization of the periodic Callahan^Hoffman^Meeks surfaces in terms of their symmetries. Mathematics Subject Classi¢cations (2000). Primary 53A10; Secondary 53C42. Key words. Periodic minimal surfaces, immersions, di¡erential geometry.
Huge Singly Periodic Minimal Surfaces in R³ And Symmetries
, 1998
"... F13.54> OE 3 ) ' where e OE 1 = 1 2 (1 \Gamma eg 2 )e!; e OE 2 = i 2 (1 + eg 2 )e!; e OE 3 = e ge!; (0.1) are holomorphic oneforms on f M satisfying 3 X i=1 j e OE j j 2 6= 0: 1 Singly Periodic Minimal Surfaces 139 140 Francisco Martin and Domingo Rodriguez We label the pair ..."
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F13.54> OE 3 ) ' where e OE 1 = 1 2 (1 \Gamma eg 2 )e!; e OE 2 = i 2 (1 + eg 2 )e!; e OE 3 = e ge!; (0.1) are holomorphic oneforms on f M satisfying 3 X i=1 j e OE j j 2 6= 0: 1 Singly Periodic Minimal Surfaces 139 140 Francisco Martin and Domingo Rodriguez We label the pair (eg; e !) as the Weierstrass representation of f M . We can work with the quotient M = f M=T , and so we have a minimal immersion x
On a Variety of Minimal Surfaces Invariant under a Screw Motion
"... Abstract. In this paper, we will prove that a certain class of branched multivalued minimal surfaces invariant under a translation or a screw motion becomes a real analytic variety via their Weierstrass data. We also prove that the class contains complex analytic variety and give a lower bound of i ..."
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Abstract. In this paper, we will prove that a certain class of branched multivalued minimal surfaces invariant under a translation or a screw motion becomes a real analytic variety via their Weierstrass data. We also prove that the class contains complex analytic variety and give a lower bound of its dimension. 1.