Format:
vi, 77 Seiten
,
Illustrationen
ISBN:
9781470441616
Series Statement:
Memoirs of the American Mathematical Society volume 264, number 1283 (sixth of 6 numbers)
Content:
The aim of this work is to adapt the complex analytic methods originating in modern Oka theory to the study of non-orientable conformal minimal surfaces in for any . These methods, which we develop essentially from the first principles, enable us to prove that the space of conformal minimal immersions of a given bordered non-orientable surface to is a real analytic Banach manifold (see Theorem 1.1), obtain approximation results of Runge-Mergelyan type for conformal minimal immersions from non-orientable surfaces (see Theorem 1.2 and Corollary 1.3), and show general position theorems for non-orientable conformal minimal surfaces in (see Theorem 1.4). We also give the first known example of a properly embedded non-orientable minimal surface in ; a Möbius strip (see Example 6.1).All our new tools mentioned above apply to non-orientable minimal surfaces endowed with a fixed choice of a conformal structure. This enables us to obtain significant new applications to the global theory of non-orientable minimal surfaces. In particular, we construct proper non-orientable conformal minimal surfaces in with any given conformal structure (see Theorem 1.6 (i)), complete non-orientable minimal surfaces in with arbitrary conformal type whose generalized Gauss map is nondegenerate and omits hyperplanes of in general position (see Theorem 1.6 (iii)), complete non-orientable minimal surfaces bounded by Jordan curves (see Theorem 1.5), and complete proper non-orientable minimal surfaces normalized by bordered surfaces in -convex domains of (see Theorem 1.7).
Note:
Literaturverzeichnis: Seite 73-77
Language:
English
Subjects:
Mathematics
Keywords:
Differentialgeometrie
;
Affiner Raum
;
Holomorphie
Author information:
Forstnerič, Franc 1958-
