Calabi-Yau domains in three manifolds

• Autores: Francisco Martín Serrano
• Localización: American journal of mathematics, ISSN 0002-9327, Vol. 134, Nº 5, 2012, págs. 1329-1344
• Idioma: inglés
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• Resumen

  • We prove that for every smooth compact Riemannian three-manifold $\overline{W}$ with nonempty boundary, there exists a smooth properly embedded one-manifold $\Delta \subset W={\rm Int}(\overline{W})$, each of whose components is a simple closed curve and such that the domain ${\mathcal D} = W - \Delta$ does not admit any properly immersed open surfaces with at least one annular end, bounded mean curvature, compact boundary (possibly empty) and a complete induced Riemannian metric.