On singly-periodic minimal surfaces with planar ends

Pérez, Joaquín

doi:10.1090/S0002-9947-97-01911-9

On singly-periodic minimal surfaces with planar ends
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by Joaquín Pérez PDF

Trans. Amer. Math. Soc. 349 (1997), 2371-2389 Request permission

Abstract:

The spaces of nondegenerate properly embedded minimal surfaces in quotients of ${\mathbf R}^3$ by nontrivial translations or by screw motions with nontrivial rotational part, fixed finite topology and planar type ends, are endowed with natural structures of finite dimensional real analytic manifolds. This nondegeneracy is defined in terms of Jacobi functions. Riemann’s minimal examples are characterized as the only nondegenerate surfaces with genus one in their corresponding spaces. We also give natural immersions of these spaces into certain complex Euclidean spaces which turn out to be Lagrangian immersions with respect to the standard symplectic structures.

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