Resumen de Embedding Bordered Riemann Surfaces in 4-dimensional Riemannian Manifolds

Seokku Ko

• Any bordered Riemann surface has a conformal model in any orientable Riemannian manifold of dimension 4. Precisely, we prove that, given any bordered Riemann surface S0, there is a conformally equivalent model in a prespecified orientable 4-dimensional Riemannian manifold. A model can be constructed by deforming a compactification surface of the given topologically equivalent complete Riemann surface S in the normal direction. This result along with previous Ko Embedding theorem(see "Embedding bordered Riemann surfaces in Riemannian Manifolds", Journal of Korean Mathematical Society, Vol. 30. no. 2, 1993) now shows that a bordered Riemann surface admits conformal models in any Riemannian manifold of dimension greater than or equal to 3.