The Busemann–Petty problem in hyperbolic and spherical spaces
نویسندگان
چکیده
منابع مشابه
The Busemann-petty Problem in Hyperbolic and Spherical Spaces
The Busemann-Petty problem asks whether origin-symmetric convex bodies in R with smaller central hyperplane sections necessarily have smaller n-dimensional volume. It is known that the answer to this problem is affirmative if n ≤ 4 and negative if n ≥ 5. We study this problem in hyperbolic and spherical spaces.
متن کاملCritical behavior in spherical and hyperbolic spaces
We study the effects of curved background geometries on the critical behavior of scalar field theory. In particular we concentrate on two maximally symmetric spaces: d-dimensional spheres and hyperboloids. In the first part of the paper, by applying the Ginzburg criterion, we find that for large correlation length the Gaussian approximation is valid on the hyperboloid for any dimension d ≥ 2, w...
متن کاملHyperbolic spaces in Teichmüller spaces
We prove, for any n, that there is a closed connected orientable surface S so that the hyperbolic space H almost-isometrically embeds into the Teichmüller space of S, with quasi-convex image lying in the thick part. As a consequence, H quasi-isometrically embeds in the curve complex of S.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2006
ISSN: 0001-8708
DOI: 10.1016/j.aim.2005.05.003