Margulis, G. A. Indefinite quadratic forms and unipotent flows on homogeneous spaces. (English) Zbl 0689.10026 Dynamical systems and ergodic theory, 28th Sem. St. Banach Int. Math. Cent., Warsaw/Pol. 1986, Banach Cent. Publ. 23, 399-409 (1989). [For the entire collection see Zbl 0686.00015.] This article contains the proof (using methods from ergodic theory) of Margulis’ celebrated theorem that a real indefinite quadratic form in at least 3 variables that is not proportional to a rational form assumes values arbitrary close to zero. For related further results and references see S. G. Dani and G. A. Margulis [Invent. Math. 98, No.2, 405-424 (1989)]. Reviewer: R.Schulze-Pillot Cited in 2 ReviewsCited in 20 Documents MSC: 11D75 Diophantine inequalities 22E40 Discrete subgroups of Lie groups 11E12 Quadratic forms over global rings and fields 11D85 Representation problems Keywords:flows on homogeneous spaces; unipotent orbits; minima of forms; indefinite quadratic form Citations:Zbl 0686.00015 PDFBibTeX XML