Open AccessAn analogue of minimal surface theory in ππΏ(π,π)/ππ(π§)
Author(s) -
Masatoshi Kokubu,
Masatomo Takahashi,
Masaaki Umehara,
Kotaro Yamada
Publication year - 2001
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/s0002-9947-01-02935-x
Subject(s) - algorithm , artificial intelligence , mathematics , computer science
We shall discuss the class of surfaces with holomorphic right Gauss maps in non-compact duals of compact semi-simple Lie groups (e.g. SL β‘ ( n , C ) / SU β‘ ( n ) \operatorname {SL}(n,\mathbf {C})/\operatorname {SU}(n) ), which contains minimal surfaces in R n \mathbf {R}^n and constant mean curvature 1 1 surfaces in H 3 \mathcal {H}^3 . A Weierstrass type representation formula and a Chern-Osserman type inequality for such surfaces are given.