Filling Inequalities Do Not Depend on Topology
نویسنده
چکیده
Gromov’s universal filling inequalities relate the filling radius and the filling volume of a Riemannian manifold to its volume. The main result of the present article is that in dimensions at least three the optimal constants in the filling inequalities depend only on dimension and orientability, not on the manifold itself. This contrasts with the analogous situation for the optimal systolic inequality, which does depend on the manifold.
منابع مشابه
A NEW NOTION OF FUZZY PS-COMPACTNESS
In this paper, using pre-semi-open L-sets and their inequality, a new notion of PS-compactness is introduced in L-topological spaces, where L is a complete De Morgan algebra. This notion does not depend on the structure of the basis lattice L and L does not need any distributivity.
متن کاملar X iv : 0 90 7 . 07 67 v 1 [ qu an t - ph ] 4 J ul 2 00 9 epl draft Possible Experience : from Boole to Bell
Mainstream interpretations of quantum theory maintain that violations of the Bell inequalities deny at least either realism or Einstein locality. Here we investigate the premises of the Bell-type inequalities by returning to earlier inequalities presented by Boole and the findings of Vorob’ev as related to these inequalities. These findings together with a space-time generalization of Boole’s e...
متن کاملFilling-enforced quantum band insulators in spin-orbit coupled crystals
An early triumph of quantum mechanics was the explanation of metallic and insulating behavior based on the filling of electronic bands. A complementary, classical picture of insulators depicts electrons as occupying localized and symmetric Wannier orbitals that resemble atomic orbitals. We report the theoretical discovery of band insulators for which electron filling forbids such an atomic desc...
متن کاملThe narrow topology on the set of Borel probability measures on a metrizable space
In this note we talk about the total variation metric and the narrow topology (also called the weak-* topology) on the set of Borel probability measures on a metrizable topological space. In the course of the note we define all the terms used in the previous sentence. The reason for talking about metrizable spaces rather than metric spaces in this note is to make explicit that the objects we de...
متن کاملGriffiths Inequalities for Ising Spin Glasses on the Nishimori Line
The Griffiths inequalities for Ising spin glasses are proved on the Nishimori line with various bond randomness which includes Gaussian and ±J bond randomness. The proof for Ising systems with Gaussian bond randomness has already been carried out by Morita et al, which uses not only the gauge theory but also the properties of the Gaussian distribution, so that it cannot be directly applied to t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008