Conformal immersions of prescribed mean curvature in R^3

Details Conformal immersions of prescribed mean curvature in R^3 Conformal immersions of prescribed mean curvature in R^3

2012-04-23

arxiv.org/abs/1204.5225v1

Mathematics

Differential Geometry

20 pages

Scientific paper

We prove the existence of (branched) conformal immersions F: S^2 -> R^3 with
mean curvature H > 0 arbitrarily prescribed up to a 3-dimensional affine
indeterminacy. A similar result is proved for the space forms S^3, H^3 and
partial results for surfaces of higher genus.

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