Minimal Surfaces: Stability and Finiteness

Manfredo P. do Carmo
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Manfredo P. do Carmo: Instituto Matematica Pura e Applicada

A chapter in Manfredo P. do Carmo – Selected Papers, 2012, pp 139-143 from Springer

Abstract: Abstract The last ten years have seen an intense activity on certain questions that arise in connection with the study of minimal surfaces. Among such questions one should mention those of regularity, embeddability, stability and finiteness of the number of minimal surfaces spanning a given boundary. In this lecture I would like to describe a few ideas, results and problems related to the questions of stability and finiteness. For simplicity, I will restrict myself to minimal surfaces of the topological type of the disk in a Riemannian manifold.

Keywords: Riemannian Manifold; Minimal Surface; Total Curvature; Minimal Immersion; Harmonic Extension (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-25588-5_12

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DOI: 10.1007/978-3-642-25588-5_12

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