Abstract
Let ϕ: U → ℝn +1 be a parametrized n-surface in ℝn +1. A variation of ϕ is a smooth map ψ: U x (−ɛ, ɛ) → ℝn +1 with the property that ψ(p,0) = ϕ(p) for all p ∈ U. Thus a variation surrounds the n-surface ϕ with a family of singular n-surfaces ϕs: U → ℝn +1 (−ɛ < ɛ < ɛ) defined by ϕ s (p) = ψ(p, s).
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© 1979 Springer-Verlag New York Inc.
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Thorpe, J.A. (1979). Minimal Surfaces. In: Elementary Topics in Differential Geometry. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6153-7_18
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DOI: https://doi.org/10.1007/978-1-4612-6153-7_18
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6155-1
Online ISBN: 978-1-4612-6153-7
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