Sur les surfaces de Weingarten sp�ciales de type minimal

Earp, Ricardo Sá; Toubiana, Éric

doi:10.1007/bf01236989

Cited by 22 publications

(59 citation statements)

References 8 publications

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“…Moreover, we obtain a new associated immersion ψ 1 with constant mean curvature one and Weierstrass data ( √ εh, ω). If ψ 0 is a complete immersion, then, from (19) and (20), (1 + ε|h| 2 )|ω| 2 is also a complete metric, that is, ψ 1 is a complete immersion. Thus, the study of complete BLW-surfaces in R 4 can be reduced to the study of complete immersions with constant mean curvature one.…”

Section: 2mentioning

confidence: 99%

“…Then ψ = gΩg (17)) is a BLW-surface satisfying (3) with induced metric and σ given by (19) and (20).…”

Section: Theorem 2 (Conformal Representation) I) Let S Be a Noncompamentioning

confidence: 99%

“…Moreover, if S is noncompact, then, from (16), (17), (19) and (20), its Gaussian curvature K I = K − 1 can be calculated as (23)…”

Section: Completeness Of the Immersionsmentioning

confidence: 99%

“…We call them linear Weingarten surfaces of Bryant type, in short, BLW-surfaces. These surfaces are a particular case of the special surfaces studied by Sa Earp and Toubiana in [21] (see also [17], [19] and [20]). …”

Section: Introductionmentioning

confidence: 99%

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Complete linear Weingarten surfaces of Bryant type. A Plateau problem at infinity

Gálvez

Martínez

Milán

2004

Trans. Amer. Math. Soc.

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Abstract. In this paper we study a large class of Weingarten surfaces which includes the constant mean curvature one surfaces and flat surfaces in the hyperbolic 3-space. We show that these surfaces can be parametrized by holomorphic data like minimal surfaces in the Euclidean 3-space and we use it to study their completeness. We also establish some existence and uniqueness theorems by studing the Plateau problem at infinity: when is a given curve on the ideal boundary the asymptotic boundary of a complete surface in our family? and, how many embedded solutions are there?

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Section: 2mentioning

confidence: 99%

“…Then ψ = gΩg (17)) is a BLW-surface satisfying (3) with induced metric and σ given by (19) and (20).…”

Section: Theorem 2 (Conformal Representation) I) Let S Be a Noncompamentioning

confidence: 99%

“…Moreover, if S is noncompact, then, from (16), (17), (19) and (20), its Gaussian curvature K I = K − 1 can be calculated as (23)…”

Section: Completeness Of the Immersionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Complete linear Weingarten surfaces of Bryant type. A Plateau problem at infinity

Gálvez

Martínez

Milán

2004

Trans. Amer. Math. Soc.

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“…Both authors have constructed a family of embedded (and also a family of non-embedded) complete rotational Weingarten surfaces in R 3 . They have also proved uniqueness of such surfaces (see [16], [17] and [18]). …”

Section: Introductionmentioning

confidence: 99%