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For linear actions of real reductive Lie groups we prove the Kempf-Ness Theorem about closed orbits and the Kirwan-Ness Stratification Theorem of the null cone.
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Patrick Eberlein and Michael Jablonski, Closed orbits of semisimple group actions and the real Hilbert-Mumford function , New developments in Lie theory and geometry, Contemp. Math., vol. 491, Amer. Math. Soc., Providence, RI, 2009, pp. 283–321
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