121 citations · 698 across the 35 of their papers we have counts for
35 papers
The Asymptotic Structure of Monopoles in R^3, Calorons, and ALF Instantons
Sergey A. Cherkis, Mark Stern
We study the asymptotic structure of instantons on multi-centered Taub-NUT manifolds, calorons, and monopoles on R^3. We show that, without any assumptions on symmetry breaking, th…
Lp -cohomology and the geometry of p-harmonic forms
Mark A. Stern
In this note we describe basic geometric properties of p-harmonic forms and p-coclosed forms and use them to reprove vanishing theorems of Pansu and new injectivity theorems for th…
Instantons on multi-Taub-NUT Spaces III: Down Transform, Completeness, and Isometry
Sergey A. Cherkis, Andrés Larraín-Hubach, Mark Stern
The index bundle of a family of Dirac operators associated to an instanton on a multi-Taub-NUT space forms a bow representation. We prove that the gauge equivalence classes of solu…
Instantons on multi-Taub-NUT Spaces II: Bow Construction
Sergey Cherkis, Andrés Larraín-Hubach, Mark Stern
Unitary anti-self-dual connections on Asymptotically Locally Flat (ALF) hyperkähler spaces are constructed in terms of data organized in a bow. Bows generalize quivers, and the rel…
On the Betti Numbers of Finite Volume Hyperbolic Manifolds
Luca F. Di Cerbo, Mark Stern
We obtain strong upper bounds for the Betti numbers of compact complex-hyperbolic manifolds. We use the unitary holonomy to improve the results given by the most direct application…
Harmonic Forms, Price Inequalities, and Benjamini-Schramm Convergence
Luca F. Di Cerbo, Mark Stern
We study Betti numbers of sequences of Riemannian manifolds which Benjamini-Schramm converge to their universal covers. Using the Price inequalities we developed elsewhere, we deri…