اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدMobius metric in sector domains
86
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The Mobius metric $delta_G$ is studied in the cases where its domain $G$ is an open sector of the complex plane. We introduce upper and lower bounds for this metric in terms of the hyperbolic metric and the angle of the sector, and then use these results to find bounds for the distortion of the Mobius metric under quasiregular mappings defined in sector domains. Furthermore, we numerically study the Mobius metric and its connection to the hyperbolic metric in polygon domains.
قيم البحث
اقرأ أيضاً
A new similarity invariant metric $v_G$ is introduced. The visual angle metric $v_G$ is defined on a domain $GsubsetneqRn$ whose boundary is not a proper subset of a line. We find sharp bounds for $v_G$ in terms of the hyperbolic metric in the partic
ular case when the domain is either the unit ball $Bn$ or the upper half space $Hn$. We also obtain the sharp Lipschitz constant for a Mobius transformation $f: Grightarrow G$ between domains $G$ and $G$ in $Rn$ with respect to the metrics $v_G$ and $v_{G}$. For instance, in the case $G=G=Bn$ the result is sharp.
We study locally compact metric spaces that enjoy various forms of homogeneity with respect to Mobius self-homeomorphisms. We investigate connections between such homogeneity and the combination of isometric homogeneity with invertibility. In particu
lar, we provide a new characterization of snowflakes of boundaries of rank-one symmetric spaces of non-compact type among locally compact and connected metric spaces. Furthermore, we investigate the metric implications of homogeneity with respect to uniformly strongly quasi-Mobius self-homeomorphisms, connecting such homogeneity with the combination of uniform bi-Lipschitz homogeneity and quasi-invertibility. In this context we characterize spaces containing a cut point and provide several metric properties of spaces containing no cut points. These results are motivated by a desire to characterize the snowflakes of boundaries of rank-one symmetric spaces up to bi-Lipschitz equivalence.
We prove in the setting of $Q$--Ahlfors regular PI--spaces the following result: if a domain has uniformly large boundary when measured with respect to the $s$--dimensional Hausdorff content, then its visible boundary has large $t$--dimensional Hausd
orff content for every $0<t<sleq Q-1$. The visible boundary is the set of points that can be reached by a John curve from a fixed point $z_{0}in Omega$. This generalizes recent results by Koskela-Nandi-Nicolau (from $mathbb{R}^2$) and Azzam ($mathbb{R}^n$). In particular, our approach shows that the phenomenon is independent of the linear structure of the space.
We compare a Gromov hyperbolic metric with the hyperbolic metric in the unit ball or in the upper half space, and prove sharp comparison inequalities between the Gromov hyperbolic metric and some hyperbolic type metrics. We also obtain several sharp
distortion inequalities for the Gromov hyperbolic metric under some families of M{o}bius transformations.
Iso-edge domains are a variant of the iso-Delaunay decomposition introduced by Voronoi. They were introduced by Baranovskii & Ryshkov in order to solve the covering problem in dimension $5$. In this work we revisit this decomposition and prove the
following new results: $bullet$ We review the existing theory and give a general mass-formula for the iso-edge domains. $bullet$ We prove that the associated toroidal compactification of the moduli space of principally polarized abelian varieties is projective. $bullet$ We prove the Conway--Sloane conjecture in dimension $5$. $bullet$ We prove that the quadratic forms for which the conorms are non-negative are exactly the matroidal ones in dimension $5$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
