Weierstrass type representation of harmonic maps into symmetric spaces

Dorfmeister, Josef; Pedit, Franz; Wu, Hongyou

doi:10.4310/cag.1998.v6.n4.a1

Cited by 243 publications

(440 citation statements)

References 22 publications

(33 reference statements)

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“…When r = 1, we will always omit the corresponding subindex. The following results are from Theorem 2.3 of [4].…”

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confidence: 99%

“…In recent years, a Weierstrass type representation [4] has been used to construct surfaces of non-zero constant mean curvature in space (CMC surfaces). This construction starts with an sl(2, C)-valued holomorphic or meromorphic 1-form on some (compact or non-compact) Riemann surface S other than S 2 .…”

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confidence: 99%

“…Let r ∈ (0, +∞). We introduce the following twisted r-loop groups (see [4], [2] and [3] for details), in which λ ∈ S 1 r serves as the loop parameter:…”

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confidence: 99%

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Unitarization of Loop Group Representations of Fundamental Groups

Dorfmeister

2007

Nagoya Mathematical Journal

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Abstract. In this paper, we give a characterization of the simultaneous unitarizability of any finite set of SL(2, C)-valued functions on S 1 and determine all possible ways of the unitarization. Such matrix functions can be regarded as images of the generators for the fundamental group of a surface in an S 1 -family, and the results of this paper have applications in the construction of constant mean curvature surfaces in space.

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“…When r = 1, we will always omit the corresponding subindex. The following results are from Theorem 2.3 of [4].…”

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confidence: 99%

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confidence: 99%

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Unitarization of Loop Group Representations of Fundamental Groups

Dorfmeister

2007

Nagoya Mathematical Journal

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“…The DPW method [4] constructs conformal CMC immersions of the universal cover M in the following three steps. Let…”

Section: Dpw Methodsmentioning

confidence: 99%

“…There is a Weierstraß type representation for this procedure, commonly referred to as the DPW method, due to Dorfmeister, Pedit and Wu [4]. The construction involves solving a linear differential system with values in a loop group and then Iwasawa decomposing the solution to obtain the extended unitary frame of the Gauss map.…”

Section: Introductionmentioning

confidence: 99%