An analogue of minimal surface theory in 𝑆𝐿(𝑛,𝐂)/𝐒𝐔(𝐧)

Kokubu, M.; Takahashi, M.; Umehara, M.; Yamada, K.

doi:10.1090/S0002-9947-01-02935-X

An analogue of minimal surface theory in $\operatorname {SL}(n,\mathbf C)/\operatorname {SU}(n)$
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by M. Kokubu, M. Takahashi, M. Umehara and K. Yamada PDF

Trans. Amer. Math. Soc. 354 (2002), 1299-1325 Request permission

Abstract:

We shall discuss the class of surfaces with holomorphic right Gauss maps in non-compact duals of compact semi-simple Lie groups (e.g. $\operatorname {SL}(n,\mathbf {C})/\operatorname {SU}(n)$), which contains minimal surfaces in $\mathbf {R}^n$ and constant mean curvature $1$ surfaces in $\mathcal {H}^3$. A Weierstrass type representation formula and a Chern-Osserman type inequality for such surfaces are given.

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