Minimal immersions of closed Riemann surfaces
Authors:
J. Sacks and K. Uhlenbeck
Journal:
Trans. Amer. Math. Soc. 271 (1982), 639652
MSC:
Primary 58E12; Secondary 53A10, 53C42, 58E20
MathSciNet review:
654854
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Abstract: Let be a closed orientable surface of genus larger than zero and a compact Riemannian manifold. If is a continuous map, such that the map induced by it between the fundamental groups of and contains no nontrivial element represented by a simple closed curve in its kernel, then there exists a conformal branched minimal immersion having least area among all branched immersions with the same action on as . Uniqueness within the homotopy class of fails in general: It is shown that for certain manifolds which fiber over the circle there are at least two geometrically distinct conformal branched minimal immersions within the homotopy class of any inclusion map of the fiber. There is also a topological discussion of those manifolds for which uniqueness fails.
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 , Topics in the real analytic theory of Teichmüller space, mimeographed notes, Univ. of Illinois at UrbanaChampaign.
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 D. Sullivan, Travaux de Thurston sur les groupes quasiFuchsiens et les variétés hyperboliques de dimension fibrées sur , Séminaire Bourbaki, 32e année (1979/80), no. 554, pp. 117.
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DOI:
http://dx.doi.org/10.1090/S00029947198206548548
PII:
S 00029947(1982)06548548
Article copyright:
© Copyright 1982
American Mathematical Society
