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On the Existence of Embedded Minimal Surfaces of Higher Genus with Free Boundaries in Riemannian Manifolds

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Variational Methods for Free Surface Interfaces

Abstract

In this chapter we consider the following configuration: a Riemannian manifold X of bounded geometry, some closed Jordan curves Γ j , and a supporting surface ∂K, disjoint from the Γ j . We further assume that the Γ j are contained in a suitable barrier ∂A of nonnegative mean curvature (cf. §2 for details).

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© 1987 Springer-Verlag New York Inc.

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Jost, J. (1987). On the Existence of Embedded Minimal Surfaces of Higher Genus with Free Boundaries in Riemannian Manifolds. In: Concus, P., Finn, R. (eds) Variational Methods for Free Surface Interfaces. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4656-5_7

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  • DOI: https://doi.org/10.1007/978-1-4612-4656-5_7

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-9101-5

  • Online ISBN: 978-1-4612-4656-5

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