91 citations · 276 across the 48 of their papers we have counts for
8 papers · 1 filter
Positive scalar curvature on manifolds with boundary and their doubles
Jonathan Rosenberg, Shmuel Weinberger
This paper is about positive scalar curvature on a compact manifold with non-empty boundary . In some cases, we completely answer the question of when has a pos…
On Gromov's compactness question regarding positive scalar curvature
Shmuel Weinberger, Zhizhang Xie, Guoliang Yu
In this paper, we give both positive and negative answers to Gromov's compactness question regarding positive scalar curvature metrics on noncompact manifolds. First we construct e…
Relative systoles of relative-essential 2-complexes
Karin U. Katz, Mikhail G. Katz, Stephane Sabourau +2
We prove a systolic inequality for the phi-relative 1-systole of a phi-essential 2-complex, where phi is a homomorphism from the fundamental group of the complex, to a finitely pre…
E_7, Wirtinger inequalities, Cayley 4-form, and homotopy
Victor Bangert, Mikhail G. Katz, Steven Shnider +1
We study optimal curvature-free inequalities of the type discovered by C. Loewner and M. Gromov, using a generalisation of the Wirtinger inequality for the comass. Using a model fo…
Isometries, rigidity, and universal covers
Benson Farb, Shmuel Weinberger
We classify all closed, aspherical Riemannian manifolds M whose universal cover has indiscrete isometry group. One sample application is the theorem that any such M with word-hyper…
Hidden symmetry and arithmetic manifolds
Benson Farb, Shmuel Weinberger
A "hidden symmetry" of a Riemannian manifold M is an isometry of a d-sheeted, 1<d<\infty, Riemannian cover of M which is not the lift of any isometry. In this paper we characterize…