Isometries of length 1 in purely loxodromic free kleinian groups and trace inequalities
Küçük Resim Yok
Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Tubitak Scientific & Technological Research Council Turkey
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In this paper, we prove a generalization of a discreteness criteria for a large class of subgroups of PSL 2(C). In particular, given a finitely generated purely loxodromic free Kleinian group Gamma = for n >= 2, we show that |trace(2) (xi(i)) - 4| + |trace(xi(i)xi(j)xi(-1)(i) xi(-1)(j)) - 2| >= 2 sinh(2) ( 1/4 log alpha(n)) for some xi(i) and xi(j) for i not equal j in Gamma provided that certain conditions on the hyperbolic displacements given by xi(i), xi(j) and their length 3 conjugates formed by the generators are satisfied. Above, the constant alpha(n) turns out to be the real root strictly larger than (2n-1)(2) of a fourth degree integer coefficient polynomial obtained by solving a family of optimization problems via the Karush-Kuhn-Tucker theory. The use of this theory in the context of hyperbolic geometry is another novelty of this work.
Açıklama
Anahtar Kelimeler
Free Kleinian Groups, Jorgensen's İnequality, Trace İnequalities, Hyperbolic Displacements, Log 3 Theorem, Karush-Kuhn-Tucker Theory, Deformation Spaces, Boundaries
Kaynak
Turkish Journal of Mathematics
WoS Q Değeri
N/A
Scopus Q Değeri
Q2
Cilt
48
Sayı
2
